The performance analysis of a fuel pump for a liquid rocket engine has been performed numerically on its design condition. A commercial three-dimensional Navier-Stokes flow solver has been used for the computation. All of the fuel pump components - inducer, impeller, volute and secondary flow passages - are included in computation for the accurate estimation of the leakage flow rate which affects the performance and axial thrust. A pitchwise-averaged mixing plane method was used on the boundaries among the fuel pump components to save computational time. The predicted overall performance satisfied the design requirement. However, the axial thrust exceeded a permissible limit. In order to reduce the axial thrust, the secondary flow passage design has been changed. With this change, the axial thrust level has been reduced to 30% as compared with the original value.