This study investigates the response of a typhoon model to the change of the sea surface temperature (SST) throughout the model integration. The SST change is parameterized as a formulae of which the magnitude is given as a function of not only the intensity and the size but the moving speed of tropical cyclone. The formulae is constructed by referring to many previous observational and numerical studies on the SST cooling with the passage of tropical cyclones. Since the parameterized cooling formulae is based on the mathematical expression, the resemblance between the prescribed SST cooling and the observed one during the period of the numerical experiment is not complete nor satisfactory. The agreements between the prescribed and the observed SST even over the swath of the typhoon passage differ from case to case. Numerical experiments are undertaken with and without prescribing the SST cooling. The results with the SST cooling do not show clear evidence in improving the track prediction compared to those of the without-experiments. SST cooling in the model shows its swath along the incomplete simulated track so that the magnitude and the distribution of the sea surface cooling does not resemble completely with the observed one. However, we have observed a little improvement in the intensity prediction in terms of the central pressure of the tropical cyclone in some cases. In case where the model without the SST treatment is not able to yield a correct prediction of the filling of the tropical cyclone especially in the decaying stage, the pulling effect given by the SST cooling alleviates the over-deepening of the model so that the central pressure approaches toward the observed value. However, the opposite case when the SST treatment makes the prediction worse may also be possible. In general when the sea surface temperature is reduced, the amount of the sensible and the latent heat from the ocean surface become also reduced, which results in the weakening of the storms comparing to the constant SST case. It turns out to be the case also in our experiments. The weakening is realized in the central pressure, maximum wind, horizontal temperature gradient, etc.