The purpose of this paper is to find the optimum design of a typical gas turbine exhaust diffuser. In order to access the maximum overall static pressure recovery at the condition of swirling flow, an evolutionary algorithm is used. The optimization process is studied in three independent cases. Firstly, the optimization is done for a single profile of strut cover from hub to shroud. Secondly, two profiles are selected for the strut covers, one in the hub section and the other in the shroud section. Finally, the optimization process is done for the strut cover and diffuser channel geometries simultaneously. In order to produce the strut cover profiles the PARSEC parameterization method is used. The turbulent 3D flow is solved using computational fluid dynamic (CFD). The optimization process starts with the initial sampling of solution domain and subsequently the genetic algorithm (GA) is used to find the global optimum. The swirling flow at the turbine exit with the Reynolds number of 1.7 ×105 based on the hydraulic diameter of the diffuser inlet is optimized. All steps of GA and corresponding processes of model creation, mesh generation by TurboGrid, flow simulation by ANSYS CFX and goal function calculation for all members of each generation are coded in the MATLAB platform. As a result of the optimization, the pressure recovery coefficients increased 1.94%, 3.1% and 7.42% in the first, second and third cases of the optimization process respectively.