A bumper system for a motor vehicle includes a bumper cross member which is arranged transversely to a travel direction and has two attachment zones for connection to two side rails arranged in parallel relationship to the travel direction. The bumper cross member has a center portion extending between the attachment zones and two end zones to close off the bumper cross member to vehicle sides. A deformation element is arranged behind each of the end zones and constructed to support in the event of a head-on collision with slight overlap the end zone which undergoes a buckling as a result of the head-on collision. At least one belt element at least partly surrounds a circumference of the deformation element and is secured to at least one of the side rails.