The invention relates to a composite damping device for vibration and noise reduction of gear shafting, which belongs to the technical field of damping devices. The composite damping device acts on each gear shaft through an auxiliary bearing, a clamp and a vibration transmission frame with a flexible structure, vibration, which is generated by some factors in a process of transmission, of a gear pair is transferred to the auxiliary bearing, and the clamp and the vibration transmission frame so as to drive a piston soaked in high-viscosity damping liquid to do shearing motion in the damping liquid, generate a damping force large enough and absorb and dissipate vibration energy, thereby suppressing bending vibration of the shaft. On one hand, internal excitation of the whole gear is reduced, on the other hand, vibration which is transferred to a gearbox body is attenuated. By virtue of the composite damping device disclosed by the invention, the vibration of frequency components due to meshing impact in the gear shafting can be simultaneously reduced, and a vibration frequency band is wide. The composite damping device has the advantages of simple structure, easiness in removal and installation, flexibility of installation position, no worn parts, long service life and the like.