The utility model discloses a damping belt pulley and an engine with the same. The damping device comprises a hub, a first rubber ring, an outer ring and an axial damping mechanism, wherein the firstrubber ring is arranged between the hub and the outer ring, the axial vibration reduction mechanism comprises an inertia ring and a second rubber ring, the inertia ring is fixedly connected with the second rubber ring, and the inertia ring and the second rubber ring are fixed to the vibration reduction belt wheel in the axial direction of the vibration reduction belt wheel. The vibration reductionbelt pulley can well reduce vibration of the vibration reduction belt pulley in the axial direction and vibration of the vibration reduction belt pulley in the bending direction, and the NVH performance of a vehicle is improved.