At the age of twenty-four Leif was asked to captain his first voyage. This was to bring gifts to King Olaf in Norway. Many preparations were made and Leif was very excited. Leif took along a crew of fourteen and Thyrker.

The wind Leif was sailing on was fair at the beginning, but after their first day it slowed only to a gentle breeze. It was five days before they sighted Iceland. Most voyages make it in two. The crew wanted to go ashore but Leif would not let them, so they kept sailing. They sailed for many days and Leif thought they would run out of food. Finally they sighted some small islands, the Hebrides, they realized they had sailed farther south than they had intended.

The day they arrived, a storm came in and didn't allow them to leave for a month. During this time Leif stayed in the house of the lord of the island. There lived the lord's daughter who was named Thorgunna. She was known to embroider tapestries and was believed to be learned in witchcraft.

Before Leif left for Norway Thorgunna told Leif she was going to have his baby and she foresaw that it would be a boy. She had her child and named him Thorgils. Later he traveled to Greenland and Leif accepted him as his son. This is the only child known to be Leif's.