Sediment transport under waves is one of the key dynamic processes of coastal sediment motion. Previous studies for this issue are mainly based on linear wave theory and quasi-steady simplification. However, waves in real circumstance are always irregular, generally with a certain degree of asymmetry and/or velocity-leaning especially in shallow water. It is envisaged that sediment movement under non-harmonic waves is different from sinusoidal waves. Based on large eddy simulation of turbulent flows in wave boundary layer, a modified method is proposed to calculate sediment transport rate under non-harmonic waves. It is further used to explore the influences of flow acceleration and the phase lead between the free stream velocity and bed shear stress on sediment transport rate in different phases of one wave cycle for forth-leaning. The net transport rate is found to increase with the degree of asymmetry and velocity-leaning index. Both the acceleration and the phase lead have a great influence on average transport rate in each phase.