A non-linear effect due to self-interaction like in the Stokes' wave is discussed on propagation of the Kelvin's ship wave from the view point of the perturbation method under the assumption of thin ship. The main purpose of this paper is to improve the expression of the phase function of the Kelvin's ship wave by considering the varying magnitude of the first order solution in the thin ship theory, whose decreasing rate is R ^-1/2 inside the cusp line of the Kelvin's wave or R ^1/3 on it, where R is the distance from the source of the wave. It is shown that the difference of the phase function from the first order solution increases in correspondence with log R inside the cusp line and with R ^-1/3 on it. Calculated bow wave pattern of Wigley model is compared with an experimental result and the result of the thin ship theory.