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Using the linear wave theory, the distributions of the wave-induced excess momentum fluxes over depth at the arbitrary wave angle and their asymptotic forms for deep and shallow water are developed. Results indicate that the distribution of the wave-induced excess momentum fluxes over depth is non-uniform and the contributions of the component below the wave trough to the total momentum fluxes become considerable in shallow water. On the basis of the Navier-Stokes equations, the simplified three-dimensional mathematical model is established by taking a phase average over a wavelength. It is found that there are the terms of the wave-induced excess momentum fluxes varying over depth in the model, which illustrates the situation of wave-current interactions and the vertical structure of current velocity are changed because of different wave-induced excess momentum fluxes at various vertical location. The finite difference method is employed to solve the simplified model. Performances of the two-dimensional vertically integrated equations are evaluated against available numerical and experimental results including the cases of wave set-up on a plane beach, longshore current due to an oblique wave, wave-induced nearshore circulation in a semi-enclosed seas, and wave-current interactions. All cases yield satisfactory agreements. The three-dimensional mathematical model is applied to the numerical simulation of wave-current interactions, and it performs well in predicting the vertical velocity structure and the plane flow field.