A jazz bass player, best known as one of the founder members of Oregon, an innovative acoustic jazz group that includes world influences.

He had early classical training in piano until the age of 13, but switched to bass in the school orchestra, experimenting with jazz and free improvisation on his own. His performing career began at age 14 with the Young Oregonians in Portland, Oregon where he met and played with American Indian saxophonist, Jim Pepper. He graduated with an arts degree from the University of Oregon where he also studied the cello. His formal bass instruction started after college with several different teachers in the US and Europe.

He was a freelance bass player in New York in the mid-1960s and was a member of Paul Winter's Consort in 1970, which he left to form Oregon with Ralph Towner, Paul McCandless and Collin Walcott.

In addition to his work with Oregon, Moore has recorded with Annette Peacock, Larry Coryell, Ralph Towner and Zbigniew Seifert, plus duets with singer Nancy King (as King & Moore). He has also worked with many jazz greats including Paul Bley, Jan Hammer, Bill Evans, Gary Burton, Elvin Jones, Tony Williams, Charlie Haden and Dave Holland.

Moore's playing tends to be on the introspective side with thoughtful and melodic improvisations that are open to the influence of folk, classical, and ethnic music.