A prediction method for pitch-damping force and moment coefficients is presented in the unified framework of the unsteady Navier-Stokes equations with the k-omega turbulence equations. This approach does not require modification of the governing equations other than the addition of noninertial force terms. The present method is applied to compute the pitch-damping coefficients using the lunar coning and the zero-spin coning motions. Grid refinement and parametric studies are performed. The computed pitch-damping coefficients and Magnus moment coefficients are in good agreement with both the parabolized Navier-Stokes data and the experimental data. The direct unsteady predictions are performed and compared with the steady coning motions. The results show that the present steady and unsteady approaches can be successfully applied to the prediction of the pitch-damping coefficients.