Numerical simulations have been used in this paper to study the propulsion device of a wave glider based on an oscillating hydrofoil, in which the profile of the pitching and heaving motion have been prescribed for the sake of simplicity. A grid model for a two-dimensional NACA0012 hydrofoil was built by using the dynamic and moving mesh technology of the Computational Fluid Dynamics (CFD) software FLUENT and the corresponding mathematical model has also been established. First, for the sinusoidal pitching, the effects of the pitching amplitude and the reduced frequency were investigated. As the reduced frequency increased, both the mean output power coefficient and the optimal pitching amplitude increased. Then non-sinusoidal pitching was studied, with a gradual change from a sinusoid to a square wave as the value of β was increased from 1. It was found that when the pitching amplitude was small, the trapezoidal pitching profile could indeed improve the mean output power coefficient of the flapping foil. However, when the pitching amplitude was larger than the optimal value, the non-sinusoidal pitching motion negatively contributed to the propulsion performance. Finally, the overall results suggested that a trapezoidal-like pitching profile was effective for the oscillating foil of a wave glider when the pitching amplitude was less than the optimal value.