Head airbag system for a vehicle and vehicle with a head airbag system

The invention relates to a head airbag system for a vehicle, comprising a gas bag (10) which can be unfolded from a stowed position into a restraint position and which has two opposite end regions (12, 14) that are connected to one another by means of a connecting element (16) attached to these regions, wherein the end regions (12, 14) are arranged opposite one another with respect to a main unfolding direction (Z) of the gas bag (10); the connecting element (16) is designed and attached to the end regions (12, 14) in such a manner that in an unfolded restraint position of the gas bag (10) the distance between the end regions (12, 14) with respect to the vertical direction (Z) of the unfolded gas bag (10) is less than the length of a gas bag region extending between the end regions. The invention furthermore relates to a vehicle with a head airbag system.