A vibration damping system for an engine mounted on a vehicle has mounting elements attached to frames of the vehicle, through which elements the engine is mounted on the frames, a damping weight provided outwardly of the engine, and a weight support unit fixed at one end thereof to the engine and having the damping weight attached at the other end thereof. The weight support unit includes a first arm extending along one lateral side of a vertical plane extending through an axis of a crankshaft and a second arm extending along the other lateral side of the vertical plane. The damping weight is attached to free ends of the arms. The damping weight is positioned above the cylinder head of the engine to extend transversely of the vertical plane.