A three-dimensional time-domain panel method is developed, which solves the Neumann-Kelvin linearised ship motions problem. The initial boundary value problem is expressed as an integral equation using the transient free surface Green's function. This integral equation is discretised using plane elements, on which the potential assumed to be constant. The memory part of the Green's function and its spatial derivatives are evaluated using fourth order ordinary differential equations, including forward speed effects. It is shown that this method is much more efficient, and as accurate, as using classical quadrature methods. The effect of the forward speed on the evaluation of the memory part of the Green's function is also investigated. Impulse response functions for the radiation, as well as the diffraction problem, are evaluated directly in the time-domain. It is shown that when a non-impulsive input is used, the radiation impulse response functions can be evaluated without resorting to Fourier transform techniques. These impulse response functions are used in convolution integral formulation of equations of motion in the time-domain in order to calculate the responses of the vessel. Impulse response functions, hydrodynamic coefficients and RAOs obtained by the time-domain method are compared with other frequency and time-domain predictions. Different bodies and vessel types are considered for zero and forward speed.