Computational fluid dynamic analysis was conducted with a new proposed Savonius hydrokinetic turbine with a parabolic blade shape specifically geared toward a small-scale power extraction. This parabolic blade geometry was developed by manipulating a couple of disparate kinds of blades in the recent past i.e. semicircular and arc shaped followed by a straight arc. The developed hydrokinetic turbine was tested numerically in a symmetric channel and its performance was evaluated concerning the power, thrust and torque coefficients. Simulations were also implemented with two other mentioned blades. The effects of Reynolds number at different tip speed ratios on the dynamic and static performance of all three models were discussed as well. The present investigation demonstrated a gain of 7.7% and 12% in maximum power coefficient with the new proposed Savonius hydrokinetic turbine by parabolic blade shape than that of the arc shaped followed by a straight arc and semicircular, respectively. Likewise, for this new proposed turbine, the maximum value of static torque coefficient improved by 4% and 25.8% than that of the arc shaped followed by a straight arc and semicircular, severally. For all three simulated blade profiles, the best performance was experienced at an optimum value of tip speed ratio 0.98 and Reynolds number 2 × 105. However, the new proposed turbine at all Reynolds numbers and tip speed ratios in the scope of this research showed a better performance than the other simulated models.