In the summer of 1983, Elio Perlman, a 17-year-old Jewish French-Italian boy, lives with his parents in rural Northern Italy. Elio's father, a professor of archaeology, invites a 24-year-old Jewish-American graduate student, Oliver, to live with the family over the summer and help with his academic paperwork. Elio, an introspective bookworm and a musician, initially thinks he has little in common with Oliver, who appears confident and carefree. Elio spends much of the summer reading, playing piano, and hanging out with his childhood friends, Chiara and Marzia. During a volleyball match, Oliver touches Elio's back but Elio brushes it off. However, Elio later finds himself jealous upon seeing Oliver pursue Chiara.
Elio and Oliver spend more time together, going for long walks into town, and accompanying Elio's father on an archaeological trip. Elio is increasingly drawn to Oliver, even sneaking to Oliver's room to smell his clothing. Elio eventually confesses his feelings to Oliver, who tells him they cannot discuss such things. Later, in a secluded spot, the two kiss for the first time. Oliver is reluctant to take things further, and they do not speak for several days.
Elio goes on a date with Marzia and the two have sex. Elio leaves a note for Oliver to end their silence. Oliver writes back, asking Elio to meet him at midnight. Elio agrees and they sleep together for the first time. Afterwards, Oliver says to Elio, "Call me by your name and I'll call you by mine". The morning after, Elio is briefly conflicted about their encounter and takes out his sexual frustration by masturbating with a peach. When Oliver finds him, Elio cries about how little time he and Oliver have left together. Marzia confronts Elio after not hearing from him for three days. He responds coldly, hurting her.
As the end of Oliver's stay approaches, Elio's parents, who appear to be aware of the bond between the two, recommend that he and Oliver visit Bergamo together before Oliver returns to the U.S. They spend three romantic days together. Elio, heartbroken after Oliver's departure, calls his mother and asks her to pick him up from the train station and take him home. Marzia is sympathetic to Elio's feelings and says she wants to remain friends. Elio's father, observing his unhappiness, tells him that the bond he had with Oliver was rare and that he envied Elio because he never was able to have what Elio and Oliver had.
During Hanukkah, Oliver calls Elio's family to tell them he is engaged to be married to a woman he has been seeing for a few years. Elio calls Oliver by his name and Oliver responds with his; Oliver also says that he remembers everything. After the call, Elio sits down by the fireplace and stares into the flames, tearfully reflecting, as his parents and staff prepare the holiday dinner.
