To guarantee the exact control of missile warhead, it is necessary to confirm the safeties of structural and fluid/thermo dynamic view points in a rocket motor. Specially, in a rocket motor despite of shortness in operating time of the rocket motor, it occurs frequently some problems of ablation at the vicinity of the nozzle throat and failure in the system itself. In these connections, in the present study, the effect of the operating time of a rocket motor on the coefficient of convective heat transfer at the nozzle wall is investigated by numerical analysis. As a result, it is turned out that the heat transfer coefficient is largest at the just ahead of nozzle throat and decreases with the increase of operating time of the rocket motor. Furthermore, we found that the smaller the radius of curvature of throat is, the maximum coefficient of convective heat transfer becomes larger.