The optimal design of a supersonic inlet is generally performed with expensive computer analysis such as the computational fluid dynamics. Thus, the feasibility criterion was incorporated into efficient global optimization (EGO) in order to efficiently perform optimal design of a supersonic inlet in this study. The strategy of EGO incorporating feasibility criterion is to improve computational efficiency by skipping unessential updation of the Kriging surrogate model of constraint function. The surrogate model is not updated when a new sample is expected to be feasible by feasibility criterion. The efficiency of EGO incorporating feasibility criterion was demonstrated by the test functions. Then, this method was applied to the optimal design of a supersonic inlet. The objective function is the coefficient of cowl drag. The constraint functions are the pressure recovery and mass flowrate. As a result, the EGO incorporating feasibility criterion for the design of a supersonic inlet was effectively performed with lower computational cost.