Olaf Gudrødsson, or as he was named after his death Olaf Geirstad-Alf, was a legendary Norwegian king of the House of Yngling from the Ynglinga saga. He was the son of Gudrød the Hunter and the brother of Halfdan the Black. Gudrød and Olaf conquered a large part of Raumarike.

Gudrød died when Olaf was twenty years old and he and Halfdan divided their kingdom between them. Olaf took the southern part and resided in Geirstad. They only inherited Vestfold because Alfgeir took Vingulmark for himself and made his son Gandalf Alfgeirsson its king.

The Ynglinga saga relates that Olaf was a skillful man and a great warrior. He was also handsome, big and strong. He was the father of Ragnvald the Mountain-High.

During the reigns of Olaf and Halfdan the Black, Värmland started to pay tribute to the Swedish king Erik Anundsson instead.

Olaf died of illness. Tjodolf of Hvin sang about him:

Long while this branch of Odin's stem
Was the stout prop of Norway's realm;
Long while King Olaf with just pride
Ruled over Westfold far and wide.
At length by cruel gout oppressed,
The good King Olaf sank to rest:
His body now lies under ground,
Buried at Geirstad, in the mound.

After his death, he was worshipped as an elf, and was called the Geirstad-alf (the "elf of Geirstad").

A hypothesis identifies Geirstad with Gjerstad near Gokstad, and his burial with the Gokstad Ship.