The opera is set on the Island of Crete, shortly after the Trojan War.
Ilia, daughter of the defeated Trojan King Priam, expresses conflicting emotions – love for her rescuer Idamante, son of the Cretan King Idomeneo, and hatred for her father’s Greek enemies. Idamante frees the Trojan prisoners in a gesture of good will. Trojans and Cretans welcome his action, but Elettra, daughter of the Greek King Agamemnon, does not approve of Idamante’s clemency toward the enemy prisoners. Arbace, the King’s confidant, brings news that Idomeneo has been lost at sea while returning to Crete from Troy. Elettra, sensing Idamante’s love for Ilia and fearing her Trojan rival may become Queen of Crete, invokes the furies of the underworld.
In a storm at sea, Idomeneo is saved from drowning by making a vow to Neptune (God of the Sea) to sacrifice, once safely on land, the first living creature he should meet. Idamante comes looking for his father. When Idomeneo realises the youth that he must sacrifice for the sake of his vow is his own child, he orders Idamante away from him. Idamante is griefstricken by his father’s rejection. The Cretans praise Neptune for Idomeneo’s safe arrival home.