An optimum aerodynamic design method for centrifugal compressor impeller has been developed. The present optimum design method is using a genetic algorithm (GA) and a two-dimensional inverse blade design method based on a meridional viscous flow analysis. In the meridional viscous flow analysis, an axisymmetric viscous flow is numerically analyzed on a two-dimensional meridional grid to determine the flow distribution around the impeller. Full and splitter blade effects to the flow field are successfully evaluated in the meridional viscous flow analysis by a blade force modeling. In the inverse blade design procedure, blade loading distribution is given as the design variable. In the optimization procedure, the total pressure rise and adiabatic efficiency obtained from the meridional viscous flow analysis are employed as objective functions. Aerodynamic performance and three-dimensional flow fields in the Pareto-optimum design and conventional design cases have been investigated by three-dimensional Reynolds averaged Navier-Stokes (3D-RANS) and experimental analyses. The analyses results show performance improvements and suppressions of flow separations on the suction surfaces in the optimum design cases. Therefore, the present aerodynamic optimization using the inverse method based on the meridional viscous flow analysis is successfully achieved.