Shigeharu Mukai (向井滋春, Mukai Shigeharu) was born in Nagoya on January 21, 1949, and started on the trombone when he entered Atsuta High School. At Doshisha University in Kyoto he joined the Third Hard Orchestra as a freshman and a modern jazz group in his second year, then left without a degree to play professionally. In 1971 he moved to Tokyo and worked in the groups of Yoshio Otomo and Ryo Kawasaki. In 1975 he won the Shinjuku Jazz Award.

His first records are sideman dates. In August 1973 he was the second trombone in Hiroshi Fukumura's twin-trombone quintet, recorded in the studio on 22 August as Morning Flight for Three Blind Mice and live five days later as Live: First Flight for Trio Records. A year later he was on Terumasa Hino's Journey Into My Mind (1974), and in 1975 on Hino's Live In Concert and Speak To Loneliness and on Kazumi Watanabe's Endless Way.

His own debut came out the same year. For My Little Bird was recorded on 9 and 18 November 1974 at Nippon Columbia's 1st Studio in Tokyo and released on Columbia (YX-7010-N) in 1975. It is a long-form quintet record: three of its four pieces are his own, and two of them, "Departure" and "Toppu," run past fifteen minutes. He followed it within the year with A Head Wind, recorded on 5, 7, 8 and 9 August 1975 (Columbia YQ-7516-N), three compositions of his own including a 20 minute 50 second title piece that fills the whole second side, with Tomoki Takahashi on tenor and soprano saxophones, Kazuhide Motooka on piano, Hideaki Mochizuki on bass and Ryojiro Furusawa on drums. Furusawa then returned the favor on You Wanna Rain (Frasco, 1976), billed as the Furusawa Ryojiro Quartet featuring Mukai, and the trombonist made a quintet record of standards and modal repertoire for Teichiku the same year, Favorite Time, with Kazumi Watanabe on guitar, Fumio Itabashi on piano, Mochizuki on bass and the American drummer Oliver Johnson.

The late 1970s turned him toward fusion. Spacing Out (Better Days, YX-7582-ND) was issued in February 1978, with its first two tracks recorded on 29 September 1977 at Nippon Columbia's 1st Studio; its opener, "Dawn ~ Turbulence," runs 16 minutes 13 seconds, and the band includes Watanabe on guitar, Yasuaki Shimizu on tenor and soprano saxophones and Furusawa on drums. In the same month he recorded Hush-A-Bye with Takeo Moriyama's quartet at Teichiku Kaikan on 27 February 1978 (Union GU-5008), with Itabashi, the tenor saxophonist Katsumi Odagiri and Mochizuki. Hip Cruiser followed in February 1979 (Better Days YX-7588-ND), recorded on 2 to 6 October 1978; Mukai arranged all but one of its tracks, Watanabe is the guitar soloist on the title tune, and it includes a trombone and acoustic guitar reading of Jobim's "Once I Loved." In the same years he played in Watanabe's Kylyn band, heard on Kylyn and Kylyn Live (1979), and in the Latin-fusion band of Naoya Matsuoka.

In 1979 he spent a short time living in New York, and in 1980 he went back to record there. Pleasure (Better Days YX-7266-ND) was cut between 31 March and 8 April 1980 with Steve Gadd on drums, Neil Jason on bass, Jeff Mironov on guitar, Jorge Dalto and Warren Bernhardt on keyboards, Naná Vasconcelos and Raphael Cruz on percussion, and Ed Walsh on synthesizers, joined by Kawasaki on guitar and Matsuoka on keyboards. Mukai wrote six of its seven pieces, and the seventh is a Milton Nascimento tune. He played a Bach 12 trombone on this record only, and a King on all the others. The same year he was the featured guest, with Toshiyuki Honda, on Isao Suzuki's Mongolian Chant (Paddle Wheel), recorded on 20 and 21 April 1980.

On his return he put his own electric band together as Morning Flight, and Margarita (February 1981, Better Days YF-7010-ND), which he produced himself, was followed by the double live album Live 97 in December. The group was renamed Orissa for the 1982 album of that name, and Japonesia (1984, Better Days YF-7087-BD) took it into reggae and dub, with Furusawa on drums. In between came So & So (Better Days YF-7065-BD, February 1983), recorded in New York with Astrud Gilberto singing on three tracks, a rhythm section of Jorge Dalto and Eliane Elias on piano, Anthony Jackson on six-string bass, Omar Hakim on drums and Jeff Mironov on guitar, and a string section led by Harry Lookofsky. Mukai composed four of its eight pieces, one of them with lyrics by Gilberto.

In the late 1980s, by his own account, he spent two or three years touring Japan in the Japan-formed band of the drummer Elvin Jones, and the experience pulled him back into straight-ahead playing. He formed Hot Session with Itabashi, the bassist Mitsuaki Furuno and Furusawa, a quartet that recorded Grand Slam on 11 to 20 October 1987 (Denon YF-7148-ND, issued February 1988) and a second album in 1989. His own account lists Hong Kong, Macau and the Berlin and Donaueschingen festivals among the places he has played. He played the Mt. Fuji Jazz Festival every summer from 1989 to 1993, performed in Moscow in 1990, and recorded the live On the Wing at the Tokyo club Buddy in Ekoda on 24 and 25 January 1991. In 1992 he toured Brazil, Argentina and Paraguay with Yosuke Yamashita's group, and he has also described playing in Beijing and Shanghai with the band of the drummer George Kawaguchi.

His straight-ahead return was documented twice. Shigeharu Mukai J Quintet featuring Junko Onishi was recorded on 25 and 26 November 1993 at the Woodstock Karuizawa Studio and released on 23 February 1994 (Somethin' Else TOCJ-5557), with Junko Onishi on piano, Mabumi Yamaguchi on tenor saxophone, Rodney Whitaker on bass and Gregory Hutchinson on drums; Mukai wrote three of its seven pieces and co-produced it. Stance (P-Vine, PVCP-9411) is the second New York date, produced by the trombonist Yoichi Murata, with Mulgrew Miller on piano, Rufus Reid on bass, Billy Hart on drums, Nicholas Payton on trumpet and John Stubblefield on saxophone. It mixes originals with Charlie Parker and Dizzy Gillespie's "Anthropology," Freddie Hubbard's "Up Jumped Spring," Slide Hampton's "A New Thing" and Tadd Dameron's "If You Could See Me Now."

From 2000 he turned to arranging for larger and stranger instrumentations, and he took up the cello that year. Super 4 Brass (Shiosai ZiZO, SHCZ-0007, January 2001) is a four-horn, three-rhythm band with every arrangement his own, with the trumpeter Hitoshi Okano, the alto saxophonist Hidenori Midorikawa and the tenor saxophonist Makoto Oka. In 2002 he formed a chamber trio with Yosuke Yamashita on piano and Tomohiro Yahiro on percussion, issued as Hakkohzan (Shiosai ZiZO, SHCZ-0016; the name is built from the three players' names, 八尋, 向井 and 山下). Four Trombones followed in 2003, with three other trombonists, and Jazz Strings in 2004 put his trombone in front of a string quartet and three rhythm players, again with all arrangements his own. Plays Standard (Geneon, 2008) was made with the fashion designer Takeo Kikuchi as total producer, with Tomonao Hara, Atsushi Ikeda and Kazuhiko Michishita sitting in. In 2011 he produced someone else for the first time, the vocalist Nobuko Kojima's debut Stretch Over.

He played the national anthem as a solo at the professional baseball All-Star Game at Nagoya Dome in 1998, and he has taught jazz at the Senzoku Gakuen College of Music, as a visiting professor from the founding of its jazz department and as a lecturer from 2012. He turned 77 in January 2026.

Mukai's trombone is a big, bright, quick horn, and the instrument is a piece of the story: a King 3B Plus with a yellow brass bell, played through a mouthpiece that bears his own name, the Willie's Mukai IIIs. Through the 1970s he was the trombonist other bandleaders called, from Hino and Watanabe to pop sessions such as Tatsuro Yamashita's Spacy (1977), and he won Swing Journal readers' polls and critics' prizes between 1975 and 1993.

As a leader he writes and arranges, and he does both for unusual combinations. For My Little Bird and A Head Wind are open quintet forms with 15 to 20 minute pieces; Hip Cruiser and Pleasure are Latin-leaning electric fusion built on dense percussion; Japonesia reaches into reggae; Super 4 Brass, Four Trombones and Jazz Strings are arranger's records, and the string-quartet date is perhaps the clearest picture of what he was working toward after he started cello. Brazil runs through the whole catalog, from Jobim's "Once I Loved" on Hip Cruiser and Nascimento on Pleasure to the Astrud Gilberto album and his own samba and bossa pieces ("Nos Dois" is on So & So and again on Jazz Strings).

The Elvin Jones years marked a line in his work. Before them he was one of Japan's leading fusion and session trombonists; after them, in his own account, he went back to the straight-ahead tradition he began in, and the Onishi quintet record, the New York Stance with Hart, Reid and Payton, and the standards-based Plays Standard are the result. Critics Leonard Feather and Ira Gitler have named him among the most respected jazz trombonists in Japan.