The museum origin stems from a donation to the city of San Francisco by Chicago millionaire Avery Brundage, who was a major collector of Asian art.

Brundage continued to make donations to the museum, including the bequest of all his remaining personal collection of Asian art on his death in 1975.

[3] Despite Brundage's professed goal of creating a "bridge of understanding" between the U.S. and Asia, a deeper insight into his actions revealed that he held racist, sexist, and anti-Semitic beliefs that entirely contradicted the mission and values of the museum.

"[5] The museum was awarded the Japanese Foreign Minister’s Commendation for their contributions to promotion of cultural exchange through art between Japan and the United States on December 1, 2020.

In 1987 Mayor Dianne Feinstein proposed a plan to revitalize Civic Center that included relocating the museum to the Main Library.

In 1995, Silicon Valley entrepreneur Chong-Moon Lee made a $15 million donation to launch the funding campaign for a new building for the museum.

The new $160.5 million project, designed by Gae Aulenti,[11] introduced an indoor sky-lit court to provide a dramatic central core to the museum.

Designed by the branding agency Wolff Olins, the logo is an upside down A, representing the idea of approaching Asian art from a new perspective.