The son of king Hrauðungr, and brother of Agnar. Their story is told in the prose header to Grímnismál:
King Hraudung had two sons, one named Agnar, the other Geirröd. Agnar was ten, and Geirröd eight winters old. They both rowed out in a boat, with their hooks and lines, to catch small fish; but the wind drove them out to sea. In the darkness of the night they were wrecked on the shore, and went up into the country, where they found a cottager, with whom they stayed through the winter. The cottager's wife brought up Agnar, and the cottager, Geirröd, and gave him good advice. In the spring the man got them a ship; but when he and his wife accompanied them to the strand, the man talked apart with Geirröd. They had a fair wind, and reached their father's place. Geirröd was at the ship's prow: he sprang on shore, but pushed the ship out, saying,Go where an evil spirit may get thee.The vessel was driven out to sea, but Geirröd went up to the town, where he was well received; but his father was dead. Geirröd was then taken for king, and became a famous man.
Odin and Frigg were sitting in Hlidskialf, looking over all the world. Odin said,Seest thou Agnar, thy foster-son, where he is getting children with a giantess in a cave? while Geirröd, my foster-son, is a king residing in his country.Frigg answered,He is so inhospitable that he tortures his guests, if he thinks too many come.Odin replied that that was the greatest falsehood; and they wagered thereupon. Frigg sent her waiting-maid Fulla to bid Geirröd be on his guard, lest the trollmann who was coming should do him harm, and also say that a token whereby he might be known was, that no dog, however fierce, would attack him.
But that King Geirröd was not hospitable was mere idle talk. He, nevertheless, caused the man to be secured whom no dog would assail. He was clad in a blue cloak, and was named Grimnir, and would say no more concerning himself, although he was questioned. The king ordered him to be tortured to make him confess, and to be set between two fires; and there he sat for eight nights. King Geirröd had a son ten years old, whom he named Agnar, after his brother. Agnar went to Grimnir and gave him a full horn to drink from, saying that the king did wrong in causing him to be tortured, though innocent. Grimnir drank from it. The fire had then so approached him that his cloak was burnt.
At the end of the poem, Odin reveals himself. Geirröðr was sitting with his sword lying across his knees, half drawn from the scabbard, but on finding that it was Odin before him, he rose for the purpose of removing him from the fires, when the sword slipped from his hand with the hilt downwards; and the king having stumbled, the sword pierced him through and killed him. Odin then vanished, and Agnar was king for a long time after.