Born in Tyler, Texas, Barrett worked as an apprentice photojournalist for Conti-Press, in Hamburg, Germany. He then attended the Art Center College of Design in Los Angeles. He assisted various photographers before opening his own studio in 1974 in New York City with photographer David Arky (who left to be on his own in 1976). Some of their early work included the National Lampoon poster, "Are You a Nerd?" In December 2005, the Museum of Television and Radio in New York City presented an exhibit of Barrett's photography called "The Muppets Say Cheese", which ran through April 2006.