A time-domain computation method based on the hybrid method is originally developed and applied to the wave-making problems of ships both in the carm water and in waves. The fluid domain is decomposed into the near field and the far field, and the space-fixed artificial surface like side-walls of a towing tank is employed to separate them. The Rankine panel method and the Green function method are applied to two domains respectively and the solutions in both domains are combined on the artificial surface. The former makes the present method flexible to the free-surface condition and later guarantees the radiation condition for any frequency. The use of the space-fixed artificial surface makes the theory free from the line-integral which usually appears along the intersection between the free-surface and the artificial surface when the moving artificial surface is used. The method is applied to the steady and the unsteady wave-making problems of the modified Wigley model, Series-60 (C_B=0.6) and Series-60 (C_b=0.8). Through the comparison of hydrodynamic forces between computed and measured, it is confirmed that the present method is very accurate and rational for any case.