Bertrand died Saturday afternoon at Cedars-Sinai Medical Center, Jolie said in a news release. No age was provided.
Jolie, her older brother, James Haven, and her boyfriend, Brad Pitt, were at the hospital Saturday, according to the news release.
Bertrand, who had small roles in the movies "Lookin' to Get Out" in 1982 and "The Man Who Loved Women" in 1983, raised Jolie and her brother after divorcing their father, Oscar-winning actor Jon Voight, when Jolie was a toddler.
A private funeral was planned, the AP reports.
In lieu of flowers, the family asked that donations be made to the Women's Cancer Research Institute at Cedars-Sinai.