The operation of gas turbines is important for producers and consumers so that their profitability depends on their proper performance. On the other hand, the development of industrial gas turbines requires a lot of investment due to the high cost of tests and experiments. Therefore, due to the raising need to increase the efficiency of gas turbines, numerical methods have been developed to optimize turbomachines. In this research, the optimization of 2D profile of the cascade of an axial flow turbine has been performed. For the cascade, the sets of identical blades, which are repeated in a continuous manner, are stacked together and the high air flow passes through them. Each numerical optimization has three main components. These components include the introduction of parametric geometry, the production of a computational network, and solving the governing equations of the flow field, and ultimately the optimization algorithm. In this research, for the first time, a CIRCLE profile design method with 33 variables has been used to parameterize the blade geometry. The main advantage of this method is the production of blades with continuous curvature distribution, which makes the pressure and velocity distribution evenly distributed over the surface of the blade. The Gambit software has been used to generate the computational grid and the solution of the governing equations on the flow field has been made using the Ansys Fluent software. Genetic Algorithm is also has been used as an optimization algorithm, and by making an automatic connection between these components, it is possible to apply this algorithm for optimization. The reduction of total pressure losses has been considered as the objective function during optimization, and the constraint of mass flow rate, blade loading, and outlet flow angle has been imposed on the target function. In the second objective function, a constraint for the cross-sectional area of ??the blade is also has been added to the previous target function. Finally, an algorithm has been developed to optimize some various blades whose data are available, in subsonic and transonic flow regimes. For one of these blades, in the case of subsonic outlet flow, the loss reduction for the first function was 14.6% and for the second target function was 13.6%. For the same blade in the transonic flow regime, the loss rate of this blade for these two target functions was 14.7% and 10.6%, respectively. In the third case, the optimization algorithm has been used for a blade with a pressure ratio of 1.1, in which case the reduction was 9.5% and 7.5% for these two objective functions, respectively. Because of the parameters has been used to define geometry, the proposed design algorithm has more flexibility and performance than the other similar methods and converges to a higher-performance geometry in the first generations. In addition, it is possible to use this optimization method for turbine blades, compressors and various types of airfoil. Keywords: Axial flow turbine, Optimization, Cascade, Genetic Algorithm, viscous flow solve