Tom Ripley is a young man struggling to make a living in New York City. When working at a party, playing the piano in a borrowed Princeton jacket, he is approached by the wealthy Herbert Greenleaf, who believes him to be a Princeton alumnus. He asks Tom to travel to Italy to persuade Greenleaf's errant son, Dickie, to return to the United States. Ripley did not go to college at all and has never even met Dickie, but nevertheless goes along and agrees. Shortly after his arrival in Italy, Ripley meets Dickie Greenleaf and his girlfriend, Marge Sherwood. He quickly insinuates himself into their lives. Over time Dickie begins to tire of his new friend, resenting Ripley's constant presence and growing dependence, especially after he learns that Tom has been lying about their days together at Princeton. Ripley's feelings are complicated by his desire to maintain the wealthy lifestyle Greenleaf has afforded him and by his growing sexual obsession with his new friend.
As a gesture to Ripley, Greenleaf agrees to travel with him on a short holiday to Sanremo. The two hire a small boat and go sailing. They begin arguing while on board, with Dickie rejecting and mocking Ripley. Enraged, Ripley attacks Dickie, smashing him with an oar and, in the ensuing struggle, accidentally killing him. Horrified, lets the boat drift to shore with Dickie's body in his arms. He then sinks the boat, with Dickie's body still on board, to conceal his crime.
When the hotel concierge mistakes Ripley for Greenleaf, Ripley realizes he can assume Greenleaf's identity. He takes on Dickie's signature and passport, and begins living off his allowance, while at the same time carefully providing communications to Marge to make her believe that Dickie has deserted her. Greenleaf's old friend Freddie Miles visits Ripley at what he supposes to be Greenleaf's apartment in Rome. He is immediately suspicious of Ripley. When Miles discovers Ripley's scam, Ripley murders him as well and dumps the body.
Over the next few weeks, Ripley's existence becomes a 'cat and mouse' game with the Italian police and Greenleaf's friends. Ripley must alternate between his pose as Dickie Greenleaf and his true identity as Tom Ripley. His predicament is complicated by Meredith Logue, a wealthy heiress he met while traveling to Italy, who believes Ripley to be Dickie Greenleaf. Ripley eventually resumes his own identity, forges a suicide note in Greenleaf's name, and moves to Venice. In succession, Marge, Dickie's father and an American private detective confront Ripley. Marge particularly suspects Ripley of involvement in Dickie's death, and Ripley prepares to murder her. He is interrupted when Marge's friend, Peter Smith-Kingsley, enters the apartment.
Towards the end of the film, the private detective reveals that Mr. Greenleaf has decided to give Ripley a portion of Dickie's income with the understanding that certain details about his son's past not be revealed to the Italian police. Ripley goes on a cruise with Smith-Kingsley, his new lover, only to discover that Meredith Logue is also on board the cruise. Logue knows Ripley only as Dickie Greenleaf, and Ripley realizes it will be impossible to keep Smith-Kingsley from discovering that he has been passing himself off as Greenleaf, since Peter and Meredith know each other and could eventually exchange words. He cannot solve this dilemma by murdering Logue, as she is traveling with a large family who will notice her disappearance. The movie concludes with a sobbing Ripley killing Smith-Kingsley to protect his secret, and resigning himself to a solitary life without love or acceptance.