The flow-induced rotation of the modified Savonius rotor, for which the blade consists of a semicircular profile and an elliptical shape, is studied using a series of unsteady computational fluid dynamics (CFD) simulations. This study first concentrates on the validation of the numerical scheme against Blackwell's experimental data of the conventional rotor. The computed flow physics around the modified rotor with the same diameter is then analyzed and compared with that of the conventional rotor during one rotation cycle. As the result, the modified rotor is outperforming the conventional one but keeping its unique features. The modified rotor offers exceeding performance at a tip speed ratio (TSR) greater than 0.8. The new peak of the power coefficient Cp is reached at TSR = 1.4 which is a typical operating condition of the wind turbine in urban areas. The remarkable finding is that the suppression of the flow separation on the blade is an effective way to improve the rotor's aerodynamic performance. As expected, the additional elliptical profile plays a key role in increasing the positive torque and in preventing the flow separation on the blade, especially at high TSR > 0.8. Finally, this study points to not only advances the fundamental understanding of flow mechanism around the rotor but also proposes a good practical energy harvesting application in urban environments.