Diffuser’s aerodynamic performance is crucial for the centrifugal compressors, while at present the universal principles for the optimization design of the vaned diffusers are still not available. In this paper, three vaned diffusers with different inlet Mach numbers were numerically studied in order to explore new design principles for the centrifugal compressor vaned diffusers. It proved that there are practical and effective design principles for the vaned diffuser optimizations, the performance of the vaned diffuser can be improved by carefully control of two aerodynamic parameter distributions: Tangential velocity (Vt) and Meridional velocity (Vm). The vaned diffusers with subsonic, transonic and supersonic inlet conditions were optimized with the new design principles, and the peak efficiencies were increased by 4.23%, 2.15% and 2.59%, respectively. The stage pressure ratios were increased by 3.36%, 1.39% and 6.49%, respectively, and their surge margins were also improved substantially. Finally, since the Vt and Vm could affect each other during the optimization process, an interactive optimization design procedure was also presented in this paper in order to accelerate the optimization process.