The invention relates to a head airbag system for a vehicle, with a gas bag (10) unfoldable from a stowed position to a restraining position, said gas bag having two facing end sections (12, 14) connected to each other by means of a connecting element (16) fastened to said end sections, wherein the end sections (12, 14) are arranged opposite each other with respect to a main deployment direction (Z) of the gas bag (10); the connecting element (16) is formed and fastened to the end sections (12, 14) in such a way that in an unfolded restraining position of the gas bag (10) the distance between the end sections (12, 14) with respect to the vertical direction (Z) of the unfolded gas bag (10) is less than the length of a gas bag section running between the end sections. The invention further relates to a vehicle with a head airbag system.