Chatter vibration is apt to occur when machining thin-walled parts with insufficient rigidity. The harmful excitation of periodical cutting forces can be mitigated by enhancing the dynamic stiffness or increasing the damping of the part. A composite viscous damper including air damping and eddy current damping is designed, which can be attached on the thin-walled part by the vacuum. Based on the formulations of air damping and eddy current damping, the optimal equivalent viscous damping is derived for achieving the maximum critical depth of cut. Furthermore, the geometries of the damper are determined for damping a specific thin-walled part after investigating its relationship with viscous damping. The modal test indicates that the damper can suppress multiple modes of the cylindrical thin-walled part, and the amplitude of the first mode of the frequency response function (FRF) is reduced by 57%. The composite viscous damper is applied to suppress the chatter and resonant vibration of the thin-walled part during machining. Milling tests demonstrate that the machining vibration is reduced by 55% and 76% after employing single damper and four dampers, respectively.