The action takes place on the island of Crete after the Trojan War.
Captive Trojan princess mourns murdered father and missing brothers. But do not hate, and love for his son of the Cretan king Idamantu owns her heart. Idamant loves Elijah, and she wants to return for the freedom of prisoners Trojans. Electra, betrothed bride Idamanta, betrayed a fit of jealousy. Meanwhile, Arbas brings news that the Cretan king Idomeneo, returning from the walls of Troy to his homeland, died at sea. To save his life and the lives of his companions, Neptune Idomeneo vowed to bring him as a sacrifice of the first, who will meet in their native shore. The first in a hurry to greet his father Idamant.
Idomeneo consults Arbasom how to save his son. They send Idamanta with Elektra in her native Argos. Idomeneo will grant Trojan prisoners, but Elijah asks to remain in Crete. Idomeneo realizes mutual love Elijah and Idamanta. Electra happy: Idamant be hers. Once Idamant Electra and get into the ship, the angry Neptune sent a sea monster to Crete. The people running away in fear.
Despite the wrath of Neptune, Idomeneo insists on leaving Idamanta but Idamant decides to join the battle with the monster and defeats him. The High Priest of Neptune King warns of disasters that befall his people for non oath. Idomeneo is ready to sacrifice his son. Elijah wants to pay for Idamanta life. Neptune moved by her love and by the oracle commands Idomeneo leave the throne and pass it Idamantu after his marriage to Elijah. People singing the praises of the gods, but Elektra is not involved in jubilation: pursued furies of jealousy, she pierces his chest with a dagger.
Premiered on January 29, 1781 in Munich.