Robinson was born into a show business family. When she was a girl, her mother, Dolores Robinson, was working in public relations for a TV station in Philadelphia and her father, Matthew Robinson, was appearing as Gordon on PBS's "Sesame Street". Her parents divorced when Robinson Peete was six years old and she moved to Malibu with her mother. While Dolores Robinson became a powerful personal manager whose clients have, through the years, included Wesley Snipes, Rosie Perez, and Jason Patric, Holly attended school with Rob Lowe, Emilio Estevez, and C Thomas Howell. She was, in fact, voted most likely to succeed in junior high school alongside Lowe.

Robinson made her acting debut on the obscure TV series "This Is the Life" in 1975. Four years later, she had her first role in primetime, as LeVar Burton's sister in the CBS TV-movie "Dummy". Robinson went off to college at Sarah Lawrence but continued to act, making her feature debut in a small role as a school child in "Lorea and the Outlaws" (1985). The following year she was a singing member of a rock band called the Cherry Bomb in the disastrous "Howard the Duck". When the audition for "21 Jump Street" materialized, the producers were looking for a Caucasian, but the African American actress impressed them and landed the job, despite planning to pursue a singing career. During the run of the series, Robinson began singing professionally in nightclubs in New York, in Paris (with Lionel Hampton) and at various Club Meds. In 1992, she was able to combine both in her portrayal of Diana Ross in the ABC miniseries "The Jacksons: An American Dream".