In this paper, we adopt a numerical method to simulate the aerodynamic characteristics of the supersonic missile with side jet. An efficient method for solving the full Navier-Stokes equations with multi-species mixture gas is developed. In order to solve the steady-state solutions of the three-dimensional compressible Navier-Stokes equations in generalized coordinate system, an implicit scheme is adopted to combine several ingredients: lower-upper symmetric Gauss-Seidel relaxation (LU-SGS), adaptive hybrid scheme of flux vector splitting and flux difference splitting spatial operators for inviscid fluxes and central differencing for viscous fluxes. This scheme is used to simulate the supersonic missile with side jet. Its solutions are found to agree with experimental data very well.