Abstract: The design and realization of a transonic turbine cascade with low energy loss is one of the crucial problems which should be solved for designing good transonic turbines. This paper deals with the inverse design problem of transonic turbine cascade in the hodograph plane by the finite area method.In the first part of the paper the governing equation is transformed into a symmetric form which can be adopted to obtain the upstream singular solution. The boundary condition connected with the existing discontinuity in the hodograph plane is also analyzed and afterwards vertified by numerical tests.The next part describes in detail the method of solving stream function field by means of finite area method, including the integral transformation of governing equation, the finite area scheme, the particular corner finite area schemes and so on. The accuracy of solution is then briefly discussed.The program is quite simple and quick-acting. Results of calculation prove that the solution is very stable and it is not necessary to modify the mesh near sonic line or other places.Moreover, calculation shows that the solution is rather sensitive to the position of the critical point on sonic line, which should be carefully selected by designers for obtaining good cascade profiles.