Abstract: A design method of aerodynamic optimization is presented for transonic turbine cascades.The method couples Genetic Algorithms (GAs) to a inviscid flow field Euler solver and the boundary layer calculation.The objective function of the transonic turbine cascade is the minimum of loss factor.The multinomial coefficients of blade geometry are taken as design variables.RA cascade and Beizhong cascade have been used as the examples of optimizational design.It is shown that the aerodynamic performance of the transonic turbine cascades has been improved greatly with little variation of the work and the strength.