Based on the analysis and investigation of the one-dimensional, compressible flow in vaneless diffusers of centrifugal compressors, an optimized design method is developed, in which a group of differential equatiors. are expressed as constraints and the loss model as an objective functional that can be minimized with given constraints. Through the analysis of the effect of the external radius of vaneless diffusers on its isentropic efficiency, the optimum external radius of vaneless diffusers is figured out in a given range of external radius for vaneless diffusers, under which the loss in vaneless diffusers can be minimized or the isentropic efficiency maximized. Finally the influences of geometric parameter on the efficiency of vaneless diffuser are expounded and the theoretical clue and suggestion for the design of rotational vaneless diffuser are proposed.