The Savonius rotor, a drag-based vertical axis wind turbine, is characterized by its design simplicity, low noise level, self-starting ability at low wind speed and low cost. However, its low performance is always a major issue. One of the remedies of this issue is to design an optimized rotor blade profile, which has mostly been developed through trial and error approach in the literature. In this paper, an optimum blade profile is obtained by maximizing its power coefficient (CP) by coupling CFD simulations of a rotor blade profile with the simplex search technique. Since the blade profile is symmetric about its axis, half of the blade geometry is created through natural cubic spline curve using three points. Two of them are kept fixed, whereas the other one is changed through optimization technique in its every iteration using MATLAB platform. In every iteration, the blade profile is meshed using ANSYS ICEM CFD. The analysis of the blade profile is performed through ANSYS Fluent by using shear-stress transport k-ω turbulence model. A finite volume method based solver is used to solve the transient 2D flow around the wind turbine. The optimum profile of the blade is compared with the conventional profile over a wide range of tip speed ratios (TSRs) in order to check its feasibility for practical applications. The optimum blade profile is found to be better than the semicircular blade in the range of TSR = 0.6–1.