Gunnar was the son of Hámundur Gunnarsson and Rannveig Sigfúsdóttur (according to Njáls saga) or Rannveig Sigmundardóttur (according to Landnáma). He had two brothers, Kolskeggur and Hjörtur, and one sister named Arngunnur, who was the wife of Hróar Tungugoði.
He was married to Hallgerður Höskuldsdóttir of Höskuldsstaðir in Laxárdal in Dalasýsla, who was known as Hallgerður langbrók ("Hallgerður longpants"). He was her third husband. It was said that she had killed both her former husbands, but had in fact only killed the first. Their marriage was considered imprudent by Gunnar's friend Njáll Þorgeirsson, because it was caused by lust and not practicality.
Gunnar was a great warrior — he is described as nearly invincible in combat. According to Njáls saga, he was a powerful, athletic man "capable of jumping his own height in full body armour, both back and front". Like Odysseus, he was a skilled archer, and in close combat his weapon of choice was the "atgeir", which scholars consider to have been a halberd or glaive of some sort. He was also an adept swimmer, and there was supposedly no game at which he had an equal. His behaviour was always polite but firm — he gave good advice and was kindly, mild but he wasn't thought of as an intelligent man because of his way of talking but he was loyal to his friends and kept good company. He was "handsome and fair of skin and had a straight nose, turned up at its tip. He was blue-eyed and keen-eyed and ruddy-cheeked with thick hair, blond and well-combed."
Gunnar was a close friend of Njáll Þorgeirsson of Bergþórshvol and came to him often for advice. Njáll tells him not to kill two men of the same family — this would lead to his death. Njáll's prediction proves right. When Gunnar kills two family members of Gissur the White, the family seeks vengeance and the men set out to Hlíðarendi to do murder. Njáll advises Gunnar to leave Iceland and head abroad to escape them. Initially, Gunnar intends to depart, but when he sees his homestead from the distance, he is so moved by the beauty of it that he changes his mind and decides to remain behind. This leads to the epic battle in which Gunnar is killed.
At first, Gunnar manages to fight off his numerous attackers with his masterful archery. When his bowstring is broken in close quarters combat, he asks his wife Hallgerður for hair from her head to mend the bow. Gunnar had slapped her previously, and she vindictively refuses. He must thus confront his attackers in hand-to-hand combat and is killed as a result.
Gunnar Hámundarson is generally considered to be the archetypical "light hero" of the Icelandic sagas (as opposed to "dark heroes" such as Egill Skallagrímsson). His manliness, courage and heroic demeanor are exaggerated, and he seems to have no ignoble weaknesses.
Gunnar is probably the most unreservedly admired of Icelandic saga heroes: a man of heroism, energy, virtue, and — above all — unswerving loyalty to the land of his birth and love for its overpowering physical beauty. However, to many educated Icelanders, Gunnar is a humorous cliché, used to reference exaggerated or unbelievable qualities of character.