Snorri Sturluson's mother was Gudny Boedvarsdóttir and she was the daughter of Boedvar Thordarson of Gardar at Akranes. Boedvar descended from Egill Skallagrimsson, the famous poet/viking from Borg at Myrar. Gudny was a very active woman and people said that her sons, Snorri, Thordur and Sighvatur, came from a good mother and were thought to be better than the children Sturla had with other women.
Snorri Sturluson didn't grow up with his parents but was fostered at Oddi from three years age.