Fishes often use a wiggling motion to generate propulsion for swimming. The wiggling motion can be modeled by a progressive wave. In the present study, an immersed boundary method is used to simulate the flows around the wiggling hydrofoil NACA 65-010 at low Reynolds numbers, and the effects of Reynolds numbers on the propulsion generation are investigated. It is observed that, as the Reynolds number ranges from 1 to 200, both the thrust coefficient and the propulsion efficiency increase with the increase of the Reynolds number, while the power efficiency decreases. Especially in the ranges of the Reynolds number smaller than 20, the lift, thrust and power coefficients exhibit a large change. With the increase of the Reynolds number, the flow patterns around the wiggling foils become more complex: the vorticity becomes more intensive near the trailing edge and the wiggling foil produces reversed von Karman vortex streets to generate propulsion.