An elderly woman tells her granddaughter the story of a young man named Edward who has scissor blades for hands. As the creation of an old inventor, Edward is an artificially created humanoid who is almost completed. The Inventor homeschools Edward, but suffers a fatal heart attack before he can attach hands to Edward. Edward tries to put the hands on himself, but his blades destroy them. Hurt, Edward cuts the deceased inventor's face.
Some years later, Peg Boggs, a local Avon door-to-door saleswoman, visits the decrepit Gothic mansion where Edward lives. She finds Edward alone and offers to take him to her home after discovering he is virtually harmless. Peg introduces Edward to her family: her husband Bill, their young son Kevin and their teenage daughter Kim. The family come to see Edward as a kind person, though Kim is initially fearful of him.
The Boggs' neighbors are curious about their new house guest, and the Boggs throw a neighborhood barbecue welcoming Edward. Most of the neighbors are fascinated by Edward and befriend him, except for the eccentric religious fanatic Esmeralda and Kim's boyfriend Jim. Edward repays the neighborhood for their kindness by trimming their hedges into topiaries. This leads him to discover he can groom dogs' hair and later he styles the hair of the neighborhood women. One of the neighbors, Joyce, offers to help Edward open a hair salon. However, while scouting a location, Joyce attempts to seduce him, but scares him away. Joyce lies to the neighborhood women that he attempted to seduce her, reducing their trust in him. The bank refuses to give Edward a loan as he does not have a background or financial history.
Jealous of Kim's attraction to Edward, Jim suggests Edward pick the lock on his parents' home to obtain a van for Jim and Kim. Edward agrees, but when he picks the lock, a burglar alarm is triggered. Jim flees and Edward is arrested. The police determine that his period of isolation has left Edward without any sense of reality or common sense. Edward takes responsibility for the robbery, telling a surprised Kim he did it because she asked him to. Edward is shunned by those in the neighborhood except for the Boggs family.