A calculation model for Truss Spars motion response is established under the wave action by combing the potential flow theory and the modified Morison equation. The high order boundary element method is used to acquire the wave exciting force and the relevant hydrodynamic information. By numerical simulation, the surge, heave and pitch s are obtained, and the parameter analysis for influence of Morison drag coefficient on responses are conducted. The calculated results indicate that the surge and pitch motions are only sensitivity to the drag coefficient in the low frequency range, and consequently the viscous damping would play an important role when the platform undergoes 2nd order wave slow drift force. For the heave response, the heave plates installed on the Truss Spar provide large vertical viscous damping which distinctly affects the heave .