Based on the continuity and motion equations of fluid, the velocity potential functional equation of the S1 stream surface and the velocity gradient equation of the S2 stream surface were established. The flow field of the direct problem was solved by calculating the two families of stream surfaces. Based on the flow field of the direct problem, the inverse problem of centrifugal pump in drawing blade shape by point-by-point integration, thickening blade and smoothing leading edge of the blade by conformal mapping was accomplished. By using the flow field of the direct problem calculated by the impeller of the inverse problem to design the impeller, and using the impeller of the inverse problem designed by the flow field of the direct problem to calculate the flow, the final impeller was designed when the direct and inverse problems was converged. This method which applies the meridional velocity of direct problem result to inverse problem, can make up the deficiency of traditional design method by using one-dimensional flow assumption. The final impeller can distribute load equally with the characters of high efficiency and excellent cavitation performance. This method can increase the efficiency of design work and the accuracy of calculating results. The data of the blade’s surface is complete which is convenient for blade manufacturing by numerical control machine.