Laboriel was born in Mexico City. Originally a classically trained guitarist, he switched to bass guitar while studying at the Berklee College of Music. Henry Mancini encouraged Laboriel to move to Los Angeles, California and pursue a recording career. His brother was the late Mexican rock & roll singer Johnny Laboriel. Their parents were Honduran immigrants from the Garifuna coast.
Laboriel has worked with artists of many music genres including the following:
Al Jarreau, George Benson, Alan Silvestri, Alvaro Lopez and Res-Q Band, Alvin Slaughter, Don Felder, Andraé Crouch, Andy Pratt, Andy Summers, Barbra Streisand, Billy Cobham, Carlos Skinfill, Chris Isaak, Christopher Cross, Crystal Lewis, Dave Grusin, Djavan, Dolly Parton, Don Moen, Donald Fagen, Elton John, Engelbert Humperdinck, Freddie Hubbard, Hanson, Herb Alpert, Herbie Hancock, Johnny Hallyday, Keith Green, Kelly Willard, Lalo Schifrin, Larry Carlton, Lee Ritenour, Leo Sayer, Lisa Loeb, Madonna, Michael Jackson, Nathan Davis, Paul Jackson Jr., Paul Simon, Quincy Jones, Ray Charles, Ron Kenoly, Russ Taff, Stevie Wonder, and Umberto Tozzi.
When Laboriel recorded his three solo albums ‒ Dear Friends, Guidum, and Justo & Abraham, he recruited a cast of musicians that included Alex Acuña, Al Jarreau, Jim Keltner, Phillip Bailey, Ron Kenoly, and others. His son Abe Laboriel Jr. performed drums.
Laboriel was a founding member of the bands, Friendship and Koinonia. He plays live regularly with Greg Mathieson, drummer Bill Maxwell, and Justo Almario. Laboriel is now in the band Open Hands with Justo Almario, Greg Mathieson, and Bill Maxwell.
In 2005, Abraham was awarded an Honorary Doctorate of Music by the Berklee College of Music.