In the prdvious papers, the authors examined the surf-riding phenomenon of a ship in the regular following waves by the self-running model tests and reported that the surf-riding phenomenon seemed to occur at the moment when the ship speed including the oscillating component due to the surging motion reached the phase velocity of the wave. They also tried to explain the occurrence of the surf-riding by analysing the equation of surging motion, and showed that once the ship speed reached the phase velocity of the wave, then the ship was caught in a state of the statical equilibrium of the longitudinal force, and therefore after that the ship speed could not change from the wave speed. The above explanation, however, was not very clear, because the equation of surging motion was characterized by the non-linear term of the exciting force and its analytical solution could not be obtained, and it was pointed out by the discusser that the confirmation by the numerical simulation should be done about the critical condition for the occurrence of the surf-riding. In the present paper, the authors derive the expedient expression of the non-liner equation of surging motion and carry out the calculation of the numerical simulation. As the result the above critical condition for the occurrence of the surf-riding proves to be correct and the unsymmetrical periodic surging motion with a large amplitude, the behavior of the occurrence of the surf-riding, and the stable or unstable behavior of the surf-riding can be simulated. As regards the unsymmetrical surging velocity, some examples of the model tests are presented to show the qualitative agreement with the simulation. It is also clarified that in some small range of the ship speed close to the critical speed for surf-riding, the occurrence of the surf-riding or the periodic surging motion depends on the initial condition about the ship position and the surging velocity of the ship. Since the critical condition itself proves to be correct, the simple method proposed previously to estimate the critical wave height and critical ship speed need not be corrected as a guidline to avoid the dangerous surf-riding.