In this paper, the three-dimensional translating pulsating source Green function and the impulse response function method are employed to solve the time-domain radiation and diffraction forces of moderate- and high-speed displacement ships. Under the assumption of week nonlinearity ,considering the effects of nonlinear incident wave forces, restoring forces, and roll damping, a weakly nonlinear six-degree-of-freedom motion model for moderate- and high-speed displacement ships is established using the indirect time-domain method. The ship's motion response in regular waves is obtained through Fourier analysis. This paper proposes three methods for updating the transient wet hull mesh: the regenerate mesh method, the dry-wet mesh method, and the wave-cut mesh method. The motion responses of Wigley I and S175 are computed using the developed numerical method to verify its accuracy and applicability to different hull types. The results show that the proposed method can predict the motions of moderate- and high-speed displacement ships with good accuracy.