An infant stroller apparatus includes a stroller frame having a push handle, a child safety seat installed with the stroller frame, and a restraint system for holding the child safety seat with the stroller frame. The restraint system includes a holding structure disposed at a transversal position and near a rear portion of the child safety seat, and two first and second abuttal arrangements provided symmetrically at left and right sides of the child safety seat. Each first abuttal arrangement includes a bearing surface carried by one side segment, and a protruding structure connected with the child safety seat that rests on the bearing surface. The second abuttal arrangements are disposed near the front portion of the child safety seat to prevent the child safety seat from moving in a direction that raises the protruding structures out of contact with the bearing surfaces.