Renewable energy has seen significant growth in the past decades because it is sustainable, has no pollution effects, and not subject to oil or gas reserves. Hydroelectric power is the cheapest type of renewable energy worldwide, even though it had limited growth in the past decades. Oscillating-hydrofoil turbine is a new type of hydroelectric turbines operating in continuous streams of water currents. In this study, a two-dimensional, unsteady computational model was developed to predict the oscillating-hydrofoil turbine’s performance using different foil sections. This model was validated with the existing experimental data in the literature. Standard symmetric foil and non-standard foils that are bio-inspired from hummingbird wings were investigated for their impact on the turbine’s performance. Results for the lift, drag, and power coefficients for these foils were compared throughout the cycle to the NACA symmetric foil used previously. Results of the vorticity contours show that the leading-edge curvature of the foil has a significant effect on the formation of the leading-edge vortex, therefore, affecting the dynamic lift force. Furthermore, using bio-inspired foils with a slight camber, the unit’s power density and efficiency increased significantly during the upward lift stroke. However, the downward lift stroke was adversely affected, which introduced the suggestion of using two reversed foils in tandem operation to obtain maximum efficiency. The largest power coefficient was obtained for the NACA0015 foil, which was equal to 0.37, and the second-best was for the RAF-19 foil with a value of 0.368.