The story is narrated by a criminologist who, reading from a leather bound report titled, "The Denton Affair", tells the tale of newly engaged couple, Brad Majors and Janet Weiss, who find themselves lost and with a flat tire on a cold and rainy, late November evening. Seeking a phone with which to call for help at a nearby castle, Brad and Janet discover a group of strange and outlandish people who are holding an Annual Transylvanian Convention. They watch, still wet from the rain, as the Transylvanians, servants, and a tap dancing groupie dance the "Time Warp", the film's signature song.
They are soon swept into the world of Dr. Frank N. Furter, a bizarre and self-proclaimed "sweet transvestite from Transsexual, Transylvania". The ensemble of convention attendees also include servants Riff Raff, his sister Magenta, and a groupie named Columbia.
Frank claims to have discovered the "secret to life itself". In a scene inspired by the classic Frankenstein films, his creation, Rocky Horror, is brought to life. The ensuing celebration is soon interrupted by Eddie, an ex-delivery boy and partial brain donor to Rocky, who rides out of a deep freeze on a motorcycle. In a jealous rage, Frank corners him and slaughters him with an pickaxe.
Brad and Janet are shown to separate bedrooms, where each is visited and seduced in turn by Frank, posing as the opposite. Janet, upset and emotional, wanders off to look for Brad, who she discovers is with Frank via a television monitor. She discovers Rocky, cowering in his birth tank, hiding from Riff Raff, who has been tormenting him. While aiding Rocky Horror, Janet seduces him, while Magenta and Columbia view the seduction from their bedroom monitor.
After discovering that his creature is missing, Frank, Brad, and Riff Raff return to the lab, where Frank learns that an intruder has entered the building. Dr. Everett Scott, Brad and Janet's old high school science teacher, has come looking for his nephew, Eddie, but Frank suspects Dr. Scott of working for the government investigating UFOs.
Rocky and the guests are served dinner, which they soon realize has been prepared from Eddie's remains. Janet runs screaming into Rocky's arms, and is chased through the halls of the castle by a jealous Frank. Janet, Brad, Dr. Scott, Rocky, and Columbia all meet in Frank's lab, where Frank captures them with the Medusa Transducer, a machine which transforms them into living statues, and then forces them to perform in a cabaret-style floor show.
The performance is interrupted by the appearance of Riff Raff and Magenta, who stage a coup and announce their plan to return to the planet Transsexual. After explaining to Frank that he is not going back with them, they kill him, and in the process also kill Columbia and Rocky. They release the remaining earthlings — Brad, Janet and Dr. Scott — warning them to leave; after they do so, the entire castle takes off into space to return to the planet of Transsexual, in the galaxy of Transylvania.