Elizabeth Avellan was born in Caracas, Venezuela, where her grandfather, Gonzalo Veloz, pioneered commercial television. At thirteen, she moved to Houston with her family and later graduated from Rice University, where she had her first behind-the-scenes experience working as stage manager and prop master for several student productions. She moved to Austin in 1986 to work in the Office of the Executive Vice-President and Provost of the University of Texas, continuing her studies in film production, art, and architecture. There she meet Robert Rodriguez - cult filmmaker and her husband to be. Avellan worked as an animator on Rodriguez's award-winning 16mm film, Bedhead, which aired on PBS after gathering acclaim on the festival circuit.
She and Robert co-founded Los Hooligans Productions when the two began work on El mariachi (1992) in 1991. Since then, Avellan has co-produced Robert Rodriguez's From Dusk Till Dawn (1996), Desperado (1995), The Faculty (1998), and upcoming Spy Kids (2001). Besides she developed several scripts and produced with Pamela Cederquist and Rana Joy Glickman, Real Stories of the Donut Men, a dark comedy written and directed by Beeaje Quick, which premiered at the South by Southwest Film Festival in March, 1997. Additionally, Avellan served as producers' rep. with Rana Joy Glickman for Love You Don't Touch Me, a romantic comedy premiered at the 1997 Sundance Film Festival.