Act I
The Usherette, sometimes referred to as "Trixie", who works in a derelict cinema, introduces tonight's "film" in a song ("Science Fiction/Double Feature"), with masked Phantoms providing the backing vocals.

After attending the wedding of his best friend since high school (Ralph Hapschatt, now married to Janet Weiss' friend Betty Munroe), Brad Majors confesses his love to Janet Weiss ("Dammit Janet") and the two become engaged. The Narrator appears and explains that Brad and Janet are leaving Denton to visit Dr Everett Scott, their former science tutor, while driving into a rainstorm. During the trip, their car has a flat tire and they are forced to walk through the rain to seek a telephone in an old castle ("Over at the Frankenstein Place").

The Narrator explains that Brad and Janet are feeling "apprehensive and uneasy", but must accept any help that they are offered. As Brad and Janet arrive, Riff Raff, the hunchbacked handyman and live-in butler, greets them, and his sister Magenta, the maid, appears. Riff Raff, Magenta and Columbia (a groupie) speak briefly of an unlucky delivery boy named Eddie who fell victim to unfortunate circumstances because he botched a delivery, before performing the show's signature dance number ("Time Warp"). Brad and Janet try to leave at this point, but are stopped when Dr Frank-N-Furter, a pansexual, cross-dressing mad scientist, arrives. He introduces himself as "a sweet transvestite from Transsexual, Transylvania" and invites Brad and Janet up to his laboratory ("Sweet Transvestite"). As he goes up, Brad and Janet are stripped to their underwear to dry off.

Brad and Janet enter the laboratory, where Frank-N-Furter gives them laboratory coats to wear. Frank announces that he has discovered the secret to life itself. He unveils his creation, a blond, well-built man named Rocky, who is brought to life. As his bandages are removed, Rocky worries about his predicament ("The Sword of Damocles"). Frank admires Rocky's physique by singing a tribute to muscle builders ("Charles Atlas Song"/"I Can Make You a Man"). A Coca-Cola freezer in the laboratory opens to reveal Frank and Columbia's former lover, Eddie, a biker covered in surgical scars, who has been rendered a (slightly more) brain-damaged zombie, intent on rescuing Columbia, and escaping the castle while successfully causing large amounts of damage to Frank's laboratory, exhibiting signs of partially returning memory of the way he lived life in the past ("Hot Patootie – Bless My Soul"). Frank panics, forces Eddie back into the freezer and hacks him to death (his weapon of choice typically being a pick axe or chainsaw). Frank tells Rocky — the recipient of the other half of Eddie's brain — that he prefers him over Eddie ("Charles Atlas Song (Reprise)"/"I Can Make You a Man (Reprise)"), as although he and Eddie had a strong mental relationship, he had no muscle, and therefore, had to go. Brad and Janet, somewhat flustered after witnessing the re-murdering of Eddie, are then ushered to separate bedrooms for the night.

Act II
The Narrator foreshadows that Brad and Janet may be unsafe. Janet enjoys Brad's advances in her darkened bedroom before realizing that it is Frank in disguise. He convinces Janet that pleasure is no crime, and after she asks him to promise not to tell Brad, they resume their lovemaking. The scene changes to Brad's darkened bedroom, where Brad makes love to Janet before discovering that, once again, it is Frank in disguise. Frank promises not to tell Janet, but as they resume, Riff Raff interrupts on the television monitor with the message that Rocky has escaped. Janet searches for Brad in the laboratory and discovers Rocky hiding there. Checking the television monitor, Janet sees Brad in bed with Frank and seduces Rocky ("Touch-a, Touch-a, Touch-a, Touch Me"). While searching the television monitor for Rocky, the rest of the group discovers that Janet has slept with him and Brad becomes hurt and angry ("Once in a While"). Riff Raff then notifies Frank that there is another visitor entering the castle: Dr. Everett Scott, the paraplegic science tutor whom Brad and Janet intended to visit.

Dr Scott in a wheelchair is wheeled into the laboratory by Columbia, where Frank accuses him and Brad of trying to investigate his castle, knowing that Dr Scott has connections with the FBI. Dr Scott assures him that he has come in search of Eddie, who is revealed to be his nephew ("Eddie's Teddy"). Frank displays Eddie's corpse to the group and then uses a device to electronically restrain the three visitors and a rebellious Rocky to the floor ("Planet Schmanet Janet"); the inhabitants of the castle are revealed to be space aliens led by Frank, who abandoned their original mission in order to engage in kinky sex with Earthlings and work on Rocky. Magenta insists that they return to their home planet now that they have been found out; Frank refuses and, instead, declares his intentions to put on a "floor show".

Under Frank's influence, Columbia, Rocky, Brad, and Janet perform song and dance routines while clad in lingerie ("Rose Tint My World (Floor Show)"). After, Frank entices them to lose all inhibition and give in to their natural carnal instincts, resulting in everyone beginning to engage in orgiastic sex ("Don't Dream It – Be It") before Frank leads them into the rousing concluding number of the floor show ("Wild and Untamed Thing"). The show comes to an abrupt end when Riff Raff and Magenta enter, wearing spacesuits and carrying ray guns. Riff Raff declares that he is usurping Frank's authority and taking them all back to their home planet ("Transit Beam"). Frank makes a final plea for sympathy from Riff Raff, trying to make him understand his desire to spend the rest of his life having sex with Earthlings ("I'm Going Home"). Riff Raff is unmoved and guns down Columbia, Frank, and Rocky before ordering Brad, Janet, and Dr. Scott to leave.

As the trio evacuates the castle, Riff Raff and Magenta express their excitement to return to their world and do the "Time Warp" again with their fellow Transylvanians ("Spaceship"). Brad and Janet watch as the castle blasts off into outer space, confused about the implications of their sexual escapades ("Super Heroes"). To conclude his tale, the Narrator says "and crawling on the planet's face, insects called the human race, lost in time, and lost in space – and meaning." As the show ends, The Usherette returns to recount the night's events ("Science Fiction/Double Feature (Reprise)").

In the original London and Los Angeles productions, "Sweet Transvestite" came before "Time Warp". This was changed for the film version and was subsequently updated for the stage version when O'Brien revised the script for the 1990 West End revival.
"Charles Atlas Song" was replaced by a reworked version of the song, "I Can Make You a Man", for the film version. O'Brien's revision of the script in 1990 featured a hybrid of the two songs under the title "I Can Make You a Man", in the 1999 revised script this song was replaced by the film version, which continues to be used in all major productions. The reprise remains unchanged except for the title.