This paper describes an inverse design method for calculating the shape of meridional plane of centrifugal impeller. This design method permits the shroud and hub contours to be indirectly calculated by medial axis contour and constraint equations. The design process is computationally inexpensive and can conveniently modify the shroud and hub shapes as the design’s demand. Based on this design method, new constraint equations are used for a new shape design of meridional plane that lead to a uniform velocity distribution in the inlet of impeller. Numerical simulations are employed to investigate the fluid flows of centrifugal fan. After validation of the numerical strategy, the pressure and velocity distributions in centrifugal fan are illustrated. The numerical results show that the inlet performance is improved and the velocity distribution is more uniform. Furthermore, in order to understand the flow mechanism inside the centrifugal fan, the secondary flow in the blade passage and velocity distribution at the shroud and hub have been carried out a detailed investigation and study.