The Savonius wind turbine is one of the best candidates for harvesting wind energy in an urban environment, due to unique features such as compactness, simple assembly, low noise level, self-starting ability at low wind speed, and low cost. However, the conventional Savonius wind turbine with semicircular blades has a relatively low power coefficient. This work focuses on optimizing the shape of the blade of the Savonius wind turbine to further improve its power coefficient. An evolutionary-based genetic algorithm (GA) is incorporated into computational fluid dynamics (CFD) simulations, thereby coupling blade geometry definition with mesh generation and fitness function evaluation in an iterative process. Three variable points along the blade cross-section are used to define the geometry of the blade arc, and the objective function of GA is set to maximize the power coefficient. Two-dimensional flow around the wind turbine is modeled by the shear-stress transport (SST) k-omega turbulence model and solved through the finite-volume method in ANSYS Fluent. Three GA optimization runs with different population and genetic operations have been carried out to provide the optimal shape of the blade of the Savonius turbine. Compared to the wind turbine with semicircular blades, the wind turbine with optimal blades and a tip speed ratio (TSR) of 0.8 achieved significant improvement (up to 33%) on the time-averaged power coefficient. In addition, the Savonius turbine with optimal blades outperformed the one with semicircular blades at a wide range of TSR (= 0.6-1.2), suggesting that the Savonius wind turbine with optimal blades has great potential to be applied in the real urban environment. The aerodynamic forces and flow structures pertaining to both wind turbines with optimal and semicircular blades are compared and discussed, to improve our understanding on their underlying mechanisms and to further improve their performance.