Optimal aerodynamic design of an s-shape diffuser is presented in this thesis. Inverse design is one of the aerodynamic design methods that contain repetitive methods. In inverse design method, pressure distribution along walls is known and duct geometry is unknown. The geometry obtained from inverse design is optimum, if walls pressure distribution is optimized. For this purpose, first, a computer program is developed to solve boundary layer equations by integration method which is a one dimensional method and suitable for turbulent and compressible flow with inverse gradient pressure. Then, this program is incorporated into genetic algorithm that belongs to the larger algorithm evolutionary algorithms (EA). Different constraints are required for optimization that one of crucial constraints is zero gradient pressure distribution at the entry and exit of duct. Aim of optimizing walls pressure distribution is to reach a maximum static pressure recovery without separation occurrence. This optimization is done by using 6 and 8 control points. These points are the same variable points in genetic algorithm. Spline function is used to achieve pressure distribution by control points. By using 8 control points, it is expected to obtain better results. In fact, optimum pressure distribution is the result of linking boundary layer program and genetic algorithm. The obtained pressure distribution is considered as the target pressure distribution for inverse design problem. For inverse design, the ball-spine algorithm is incorporated into a turbulent viscous flow solver. Here, CFX is considered as the flow solver. The optimum geometry is obtained after the inverse design process. Through the design process, the duct geometry is changed to reach one satisfying the target pressure distribution. Finally, for different height to length ratios, the corresponding optimal shapes are computed. S-shaped and straight diffusers are considered as our test cases to be optimized in this thesis. The numerical solution of flow inside the designed S-shaped and straight diffuser shows that maximum static pressure recovery without separation is reached. Also, the results of flow analysis inside the designed geometry show that using 8 Control points for optimizing pressure distribution, is more desirable. Finally, for different height to length ratios, the corresponding optimal shapes are computed. Keywords : Inverse Design, s-shape diffuser, Genetic Algorithm, boundary layer equations