The son of gospel singer Woody Brown, Sr. grew up in Newark, New Jersey, where he began to study at the Arts High School trumpet and music theory with Jerome Ziering at the age of eleven years. Strongly impressed he was at the time of the trumpeter Clifford Brown, whose game he had experienced. Next to him were Dizzy Gillespie, Fats Navarro, Miles Davis, Kenny Dorham and Lee Morgan of importance. At the age of sixteen he dropped out of high school.
In 1963 he worked - together with Chick Corea - with Willie Bobo and Eric Dolphy. Dolphy invited him for the following year on a trip to Paris, but died just before the deadline. Shaw joined the journey alone and entered Paris and in Germany with Kenny Clarke, Bud Powell, Johnny Griffin, Art Taylor and Nathan Davis.
1965 to 1966 he was a member of Horace Silver Quintet, in the following years he played recordings with Chick Corea, Jackie McLean ( Demon's Dance 1967), Booker Ervin, McCoy Tyner and Andrew Hill one. 1968-1969 he worked with Max Roach. After working with Pharoah Sanders, Hank Mobley, Gary Bartz, Archie Shepp and Joe Henderson he had 1971-1973 an engagement with Art Blakey and the Jazz Messengers, with whom he recorded three albums. 1972 and 1978 played Shaw in The George Gruntz Concert Jazz Band.
He then went to San Francisco, where he led a band with Bobby Hutcherson and two albums grossed. In 1975 he returned to New York, where he played in the Louis Hayes - Junior Cook Quintet; In 1976, he participated in Harry Whitaker's debut album Black Renaissance. Since 1978, published by Columbia Records some of his most important albums. He has worked in time with Carter Jefferson, Onaje Allan Gumbs, Stafford James and Victor Lewis; 1980-1983 were Mulgrew Miller, Steve Turré, Stafford James and Tony Reedus members of his quintet. In 1986 he formed a new quintet, which, inter alia, Larry Willis, David Williams and Terri Lyne Carrington belonged.
His last years were marred by illness. In a subway accident, he lost an arm ten weeks later, he died of kidney failure.
2012 founded the Vienna- German trombonist Johannes Herrlich the "Woody Shaw Project" to get along with Daniel Nösig tp, Oliver Kent p, Joe Abentung b and Mario Gonzi dm at concerts in Vienna's Jazzland the current jazz audience at the style -forming instrumentalists and composers to remember.
Disco Graphical Notes
- Song of Songs ( OJC, 1972) with Bennie Maupin, George Cables
- The Moon Trane ( Muse, 1974) with Azar Lawrence, Cecil McBee, Buster Williams
- Solid ( Camden, 1974-87 ) with Kenny Garrett, Kenny Barron, Kirk Lightsey, Peter Leitch
- Rosewood (Columbia, 1977) with Steve Turre, Joe Henderson, Victor Lewis
- Lotus Flower ( Enja, 1982) with Steve Turre, Mulgrew Miller, Tony Reedus
- Night Music ( Elektra, 1983) with Steve Turre, Mulgrew Miller, Stafford James, Tony Reedus; Guest Artist: Bobby Hutch Bergersen
- Bemsha Swing Live ( Blue Note Records, 1986) with Geri Allen, Robert Hurst
- The Complete CBS Studio Recordings of Woody Shaw - (1977-1981) - ( Mosaic 1992) - 4 LPs, 3 CDs with Joe Henderson, Frank Wess, Carter Jefferson, Steve Turre, Onaje Allan Gumbs, Clint Houston, Victor Lewis, Charles Sullivan, James Spaulding, Curtis Fuller, Buster Williams, George Cables, Gary Bartz, Larry Willis, James Stafford, Mulgrew Miller, Tony Reedus