Robinson was born in Chicago, Illinois. The son of a check forger, Frank started out working as a copy boy for International Service in his teens and then became an office boy for Ziff-Davis. He was drafted into the Navy for World War II, and when his tour was over went to college where he majored in physics. Then, according to his official website, he could find no work as a writer, and wound up back in the Navy to serve in Korea, where he managed to keep writing, read a lot, and was published in the magazine Astounding.

After the Navy he went to graduate school in journalism, then worked for a Chicago-based Sunday supplement. Soon after he switched to Science Digest, where he worked from 1956-1959. From there, he moved into men's magazines: Rogue (1959-65) and Cavalier (1965-66). In 1969 Playboy asked him to take over the Playboy Advisor column. He remained with Playboy until 1973, when he left to write full time.

After moving to San Francisco in the 1970s, Robinson, who is gay, was a speechwriter for gay politician Harvey Milk; he also has a small role in the film Milk.

As of 2008, he is the author of 16 books, the editor of two others, and has penned numerous articles. Three of his novels have been made into movies. The Power (1956) was a supernatural science fiction and government conspiracy novel about people with superhuman skills, filmed in 1968 as The Power. The technothriller The Glass Inferno, co-written with Thomas N. Scortia, was combined with Richard Martin Stern's The Tower to produce the 1974 movie The Towering Inferno. The Gold Crew, also co-written Scortia, was a tense nuclear threat thriller and was filmed as an NBC miniseries re-titled The Fifth Missile.

Besides The Glass Inferno and The Gold Crew he collaborated on several other works with Scortia, including The Prometheus Crisis, The Nightmare Factor and Blow-Out. More recent works include The Dark Beyond the Stars, and an updated version of The Power (2000) which closely followed Waiting (1999), a novel with similar themes to The Power. His newest novel is a medical thriller about organ theft called The Donor.