Luigi Grasso was born in Ariano Irpino, in Italy's Avellino province, on September 28, 1986. He began saxophone at age five, originally as a doctor-recommended remedy for asthma, and was largely self-taught until he started attending Berklee College of Music clinics held at the Umbria Jazz Festival in Perugia at age eleven. That connection led to a full-tuition scholarship to Berklee's Boston summer program. In 1997, at around age eleven, he won the Italian television talent competition "Bravo Bravissimo," which launched a run of festival, club and TV appearances across Europe throughout his early teens. In 1999, at thirteen, he released his debut recording, A Love Supreme, on Java Records with the Teo Ciavarella Trio, featuring his younger brother Pasquale Grasso, then a child prodigy on guitar and today a New York-based jazz guitarist in his own right, in a credited cameo.

Grasso studied with the American guitarist Agostino Di Giorgio in Italy and, from 2001 to 2009, apprenticed closely with NEA Jazz Master Barry Harris, working as a participant and educational assistant in Harris's European master classes - a relationship that shaped his bebop vocabulary directly at the source. In 2004 he began parallel studies in classical composition, harmony and counterpoint at the Giovanni Martini Conservatory in Bologna. His first American trip came in 2008, playing New York rooms including Smalls, Fat Cat and the Iridium, and he built a lasting network there among swing and bebop musicians: Frank Wess, Kenny Barron, Bobby Durham, Leroy Williams, Steve Grossman, the Harry Allen-Joe Cohn quartet, pianist Rossano Sportiello and pianist Ehud Asherie among his credited collaborators and named influences (per his own All About Jazz biography; none of these specific pairings carries an independently verified Discogs recording credit alongside Grasso).

In 2013 he formed the Luigi Grasso Quartet with Pasquale Grasso on guitar, bassist Mathias Allamane and American drummer Keith Balla, releasing Ça Marche on the Parisian label Echopolite and touring Europe with the group; a second quartet album followed in 2014 with Ari Roland replacing Allamane on bass. The same year, he was a featured soloist on Crazy Blues (Universal), a project led by vocalist China Moses and pianist Raphael Lemonnier, and went on to serve as musical director for Moses's Nightintales. From 2010 to 2019 he lived in Paris, teaching at the conservatories of the city's 9th and 11th arrondissements alongside his own performing career. In 2018 his own ensemble, the Greenwich Session, released Invitation au Voyage on Camille Production, built around an unusual horn-and-reed orchestration (French horn, English horn, basset horn and bass clarinet alongside trumpets, saxophones, guitar, bass and drums) with Pasquale Grasso and Ari Roland in the band and guest vocals from China Moses and Paola Mazzoli. That same year he recorded the duo album A Coffee for Two with pianist Rossano Sportiello, and in 2019 he appeared as featured saxophonist on La Section Rythmique +2, a swing session led by guitarist David Blenkhorn's trio alongside tenor saxophonist Harry Allen, released on Frémeaux & Associés.

In 2019 Grasso joined the NDR Bigband in Hamburg, Germany, as a soloist, a position that placed him among the featured voices of one of Europe's leading public-broadcaster jazz orchestras; he has since appeared on the band's recordings with clarinetist Kinan Azmeh (Flow, 2021), reedman Michael Moore (Sanctuary, 2019-2020) and composer John Hollenbeck (Colouring Hockets, 2024), and performed live with the NDR Bigband at JazzBaltica. In 2020 he co-founded the jazz label LP3 45 Records with pianist Laurent Courthaliac, pianist Yaron Herman and Peter Schnur. In 2022 he was one of two featured alto soloists, alongside the WDR Big Band's own Johan Hörlén, on Birth of a Bird (Celebrating the Music of Charlie Parker), a Charlie Parker centennial tribute arranged by Mike Abene for the Cologne-based WDR Big Band. In 2023 he released Dantesca, an original suite for symphony orchestra and jazz soloist inspired by Dante's Divine Comedy, recorded with the Orchestra Senzaspine under conductor Tommaso Ussardi on his own LP3 45 label - one of the first works to pair a jazz soloist with a symphony orchestra with no jazz material quoted in the writing itself. His most recent large-scale project, La Dimora dell'Altrove, an extended work for the NDR Bigband written and conducted by Norwegian composer Geir Lysne, was performed live at JazzBaltica in 2025.

He placed second at the Premio Internazionale Massimo Urbani, first at "Bravo Bravissimo" (1997), and third at Montecarlo's International Jazz Soloist Competition.

Grasso's playing sits squarely in the bebop lineage his mentor Barry Harris embodied, and his catalogue reflects two connected career tracks. On one side is his identity as a swing-and-bebop combo player rooted in the New York small-group tradition - the duo record with Rossano Sportiello, the Frémeaux session alongside Harry Allen, the Fat Bros 5et date with fellow Italian expatriates Pasquale Grasso and Rossano Sportiello - all recorded in a mainstream, standards-and-original-tunes idiom close to his mentors Barry Harris and Frank Wess. On the other is his career as a big-band soloist and orchestral composer: featured alto chair with two of Europe's flagship radio jazz orchestras, the NDR Bigband and the WDR Big Band, and increasingly ambitious original writing for large ensembles, culminating in Dantesca's pairing of a jazz saxophone soloist with a full symphony orchestra. Across both tracks his alto tone and phrasing stay anchored in the bebop vocabulary he absorbed directly from Harris, even as the settings around him range from unaccompanied trio swing to symphonic scale.