The effect of non-sinusoidal trajectory on the propulsive performances and the vortex shedding process behind a flapping airfoil is investigated in this study. A movement of a rigid NACA 0012 airfoil undergoing a combined heaving and pitching motions at low Reynolds number (11 000) is considered. An elliptic function with an adjustable parameter S (flatness coefficient) is used to realize various non-sinusoidal trajectories. The two-dimensional unsteady and incompressible Navier-Stokes equation governing the flow over the flapping airfoil is resolved using the commercial so ware STAR CCM+. It is shown that the combination of sinusoidal and non-sinusoidal mapping motion has a great effect on the propulsive performances of the flapping airfoil. The maximum propulsive efficiency is always achievable with sinusoidal trajectories. However, non-sinusoidal trajectories are found to considerably improve the propulsive force up to 52% larger than its natural value. Flow visualization shows that the vortex shedding process and the wake structure are substantially altered under the non-sinusoidal trajectory effect. Depending on the nature of the flapping trajectory, several modes of vortex shedding are identified and presented in this paper.