Singular point distribution method is an important approach in axial blade design for computing and shaping midline of axial impeller airfoils on a developed flow plane. The principle involved in this method is to place continuous vortices along the midline to replace airfoils, to induce a plane velocity field meeting the requirement of specified pump performance, and, finally, to form the required microbending airfoil midline. A proper strength function of vortex sheet is a primary to realize this object. It is found that the commonly defined strength function is only suitable for flow conditions in runner plane airfoils. We presented a new vortex strength function differing from the traditional one and justified the reasonableness of the new theorem by potential flow theories: the resultant velocity normal to the sheet is zero, in compliance with the fact that the flow can’t penetrate the solid airfoil; the computed velocities at the front and rear points of the airfoil in a uniform stream indicate these two points are in agreement with Kutta-Chaplygin conditions. The paper formulates a new way for axial airfoil design.