Grier was born on May 26, 1949, in Winston-Salem, North Carolina, the daughter of Gwendolyn Sylvia (née Samuels), a homemaker and nurse, and Clarence Ransom Grier, Jr., who worked as a mechanic and technical sergeant in the United States Air Force. She has one sister and one brother. Grier has stated that she is of mixed ancestry, namely of African-American, Hispanic, Chinese, Filipino, and Cheyenne heritage. She was raised Catholic and later baptized as a Methodist.
Because of her father's military career, the family moved frequently during her childhood to various places such as England before eventually settling in Denver, Colorado, where she attended East High School. While in Denver, she appeared in a number of stage productions, and participated in beauty contests to raise money for college tuition at Metropolitan State College.