The Savonius wind turbine is a type of vertical axis wind turbine (VAWTs) that is simply composed of two or three arc-type blades which can generate power even under poor wind conditions. A modified Savonius wind turbine with novel blade shapes is introduced with the aim of increasing the power coefficient of the turbine. The effect of blade fullness, which is a main shape parameter of the blade, on the power production of a two-bladed Savonius wind turbine is investigated using transient computational fluid dynamics (CFD). Simulations are based on the Reynolds Averaged Navier-Stokes (RANS) equations with a renormalization group turbulent model. This numerical method is validated with existing experimental data and then utilized to quantify the performance of design variants. Results quantify the relationship between blade fullness and turbine performance with a blade fullness of 1 resulting in the highest coefficient of power, 0.2573. This power coefficient is 10.98% higher than a conventional Savonius turbine.