Suppressing the kernel migration rates under normal operation condition is quite important from the viewpoint of the fuel integrity for High-Temperature Gas-cooled Reactors. It depends on both the fuel temperature and the fuel temperature gradient. The presence of the ideal axial power distribution to minimize the maximum kernel migration rate allows us to improve the efficiency of design work. Therefore, we propose a new method based on Lagrange multiplier method in consideration of thermohydraulic design in order to obtain the ideal axial power distribution to minimize the maximum kernel migration rate. For one of the existing conceptual designs performed by JAEA, the maximum kernel migration rate for the power distribution to minimize the maximum kernel migration rate proposed in this study is lower by approximately 10% than that for the power distribution as a conventional design target to minimize the maximum fuel temperature.