[3] He had his start as an assistant to Katy Keene comic book artist Bill Woggon, who lived in the Santa Barbara, California, area Norman grew up in.

In 1957, Norman was employed as an inbetweener on Sleeping Beauty (released in 1959) at The Walt Disney Company, becoming the first African-American artist to remain at the studio on a long-term basis.

[4][7] In 1972, a different Fat Albert and the Cosby Kids Saturday morning cartoon series was produced for CBS by Filmation Associates.

[8] He has worked on motion pictures for Walt Disney Animation Studios and Pixar, having contributed creatively as a story artist on films such as The Hunchback of Notre Dame, Mulan and Dinosaur for Walt Disney Animation Studios and Toy Story 2 and Monsters, Inc. for Pixar among others, including Reel FX's Free Birds.

[11][12] Debuting at the 2017 D23 Expo, Disney Editions published the picture book A Kiss Goodnight ISBN 9781484782286 written by Richard M. Sherman and illustrated by Norman.

[13] Norman was also part of a Members Only Preview for the behind-the-scenes exhibition titled Walt Disney’s The Jungle Book: Making a Masterpiece during a special talk alongside Andreas Deja, Darleen Carr and Bruce Reitherman which took place on June 22, 2022.

[20] In 2015 Norman received the Friz Freleng Award for Lifetime Achievement for Excellence in Animation from the International Family Film Festival.