Abstract: A potential stream function method is applied to designing transonic airfoils. The flowfield is computed by solving the full potential equations with the aid of a relaxation method. An artificial density scheme has been developed to replace the type related scheme. As compared with the latter, the artificial density scheme employs an identical scheme in whole field and converges steadily. Numerical results show that this method is applicable to initial designing of compressor airfoils and provides a better approximation of the actual conditions by taking into account the effect of the axial-velocity-ratio.