The flapping hydrofoil bionic pump is an innovative hydrodynamic device that utilizes flapping hydrofoil technology. Flapping hydrofoil bionic pumps are crucial in addressing issues like inadequate river hydropower and limited water purification capabilities in flat river network regions. Optimizing the foil characteristics is essential for enhancing the hydrodynamic efficiency of the flapping hydrofoil bionic pump. This study investigates the impact of foil camber parameters on the hydrodynamic performance of swing-type asymmetric flapping bionic pumps. The NACA series standard foils with varying cambers are analyzed using the overlapping grid technology and finite volume method. The thrust coefficient, flow rate, pumping efficiency, and flow field structure of the flapping hydrofoil bionic pump are examined under pressure inlet conditions with the foil camber. The findings indicate that increasing the foil’s curvature within a specific range can greatly enhance the maximum values of thrust coefficient, propulsive efficiency, and pumping efficiency of the flapping hydrofoil bionic pump. Specifically, when the foil curvature is 6%c, the maximum value of the instantaneous thrust coefficient of the flapping hydrofoil bionic pump is significantly improved by 31.25% compared to the symmetric foil type under the condition of an oscillating frequency of f = 1 HZ. The flapping hydrofoil bionic pump achieves its maximum pumping efficiency when the oscillation frequency is within the range of f ≤ 2.5 Hz. This efficiency is 11.7% greater than that of the symmetric foil, and it occurs when the foil curvature is 8%c. Within the frequency range of f > 2.5 Hz, the flapping hydrofoil bionic pump that has a foil curvature of 6%c exhibits the highest enhancement in pumping efficiency. It achieves a maximum increase of 12.8% compared to the symmetric foil type. Nevertheless, the average head was less than 0.4 m, making it suitable for ultra-low-head applications.