La Canasta was established in 1987 by Alberto and LiLi Mier. Alberto came from Torreon, a town in Central Northern Mexico, to pursue a degree in Chemistry from San Francisco State University. After graduating in 1971, he returned to Mexico. On a vacation to the coastal city of Vera Cruz, he met LiLi, who was helping her mother Dona LiLi run a restaurant. He convinced her to join him in San Francisco, and in 1981 LiLi arrived with her family recipes and expertise in the kitchen.
Alberto and LiLi worked in catering and restaurant management for several years before deciding to start their own business. What began as a need for a kitchen for their catering enterprise, became the first La Canasta restaurant at the corner of Filbert and Fillmore. The popularity of their authentic home-made cuisine and regional specialties grew, and five years later La Canasta opened its doors at the present location on Buchanan at Union. La Canasta has catered events hosted by a variety of notable San Franciscans including George Lucas, the Aliottos, the Pelosis, and Gavin Newsom. Patrons of La Canasta include the likes of former 49er Ronnie Lott, and actors Sally Field and Hector Elizondo.