An airbag assembly (2) includes: an air bag (21), mounted to a vehicle seat (1) and capable of inflating from an undeployed state to a deployed state, wherein in the deployed state, the air bag (21) extends along the head and torso of an occupant (3) in the vehicle seat (1), so as to surround the head and torso of the occupant (3); and a strap (22), for mounting the air bag (21) to the vehicle seat (1) and having a first section (221) and a second section (222), wherein in the deployed state, the strap (22) is tightened, the first section (221) being mounted to the air bag (21) on an outer surface of the air bag (21) in an extension direction of the air bag (21), and the second section (222) extending on at least one outer side surface of the air bag (21) in a direction at an angle with respect to the extension direction of the air bag (21). Also disclosed is a vehicle seat assembly, including a vehicle seat and an airbag assembly mounted to the vehicle seat. When the air bag is deployed, the tightened strap constrains the side surfaces of the air bag, so as to reliably constrain lateral displacement of the air bag from being overly large when the air bag is subjected to lateral impact from an occupant. Thus, lateral displacement of the occupant can be effectively suppressed, thereby preventing the occupant from colliding with a nearby occupant or a vehicle interior trim.