The film opens with a mysterious stranger, his face swathed in bandages and his eyes obscured by dark spectacles, taking a room at an inn at the English village of Iping (in Sussex). Never leaving his quarters, the stranger demands that the staff leave him completely alone. However, his dark secret is slowly revealed to his suspicious landlady and the villagers: he is an invisible man. When the innkeeper (Forrester Harvey) and his semi-hysterical wife (Una O'Connor) tell him to leave after he makes a huge mess in the parlor and drives away the other patrons, he tears off the bandages, laughing maniacally, and throws the innkeeper down the stairs. He takes off the rest of his clothes, rendering himself completely invisible, and tries to strangle a police officer.
The invisible stranger is revealed as Dr. Jack Griffin (Claude Rains), a scientist who has discovered the secret of invisibility while conducting a series of tests with a strange new drug called "monocane". He returns to the laboratory of his mentor, Dr. Cranley (Henry Travers), where he reveals his secret to his fiancee Flora Cranley (Gloria Stuart), Dr. Cranley's daughter, and to his one-time partner Dr. Kemp (William Harrigan). Monocane has rendered Griffin's entire body undetectable to the human eye; alas, it also has the side-effect of driving Griffin insane. Cranley has investigated and discovered a single note about monocane (Griffin has burnt all his other papers to cover his tracks) in a now empty cupboard in Griffin's empty laboratory, and realizes that Griffin has recently used it. On the evening of his escape from the inn, Griffin turns up in Kemp's living room and imprisons him in his own house. He forces Kemp to be his partner again, and together they go back to the inn where Griffin stayed and retrieve his notebooks on the invisibility process. While there, he picks up a wooden stool and cracks the police officer over the head, killing him.
Kemp calls Cranley, asking for help, and then secretly calls the police. Flora comes to him and they talk for only a minute, until the police show up. Their conversation reveals that the two are completely devoted to each other, and she is as infatuated with him as he her. In Flora's presence, Griffin becomes more placid, and calls her "darling". He rants about power, but when he realises Kemp betrayed him to the police through the window, his first reaction is getting Flora to flee, and out of danger. She begs to let her stay, but he insists she has nothing to do but leave. After promising Kemp that at 10:00 PM the next night he will murder him, Griffin escapes again and goes on a spree of terror, running down the streets killing, robbing, and reciting nursery rhymes in a malicious voice. The police offer a monetary award for anyone who can think of a way to catch the Invisible Man.
They disguise Kemp as a police officer and lead him away from his house to protect him, but Griffin has been following them all along. He forces Kemp into the front seat of his car with his hands tied and releases the emergency brake. The car rolls down a steep hill, over a cliff, and explodes.
Finally, after derailing a train and throwing off a cliff two men who are searching for him with the police as volunteers, Griffin rests in a barn. The owner of the barn hears the sleeping Griffin stirring and sees the hay in which Griffin is sleeping inexplicably moving. The farmer goes to the police and tells them that "there's breathing" his barn. The police surround and set fire to the barn. When Griffin comes out, the police sight his footprints in the snow and open fire, mortally wounding him. Griffin is taken to hospital where, on his deathbed, he admits to Flora that he has tampered with a type of science that was meant to be left alone. The effects of the monocane wear off the moment he dies, and he becomes visible once again.