Numerical solution of the nonlinear non‐resonant interaction between two trains of gravity waves in a finite water depth is studied in this paper. Two finite Fourier series with unknown coefficients are assumed for the velocity potential and the free surface elevation. The unknown coefficients are then determined numerically by a linear Taylor differential correction technique applied iteratively to minimize the free surface boundary condition error. Numerical results up to the fifth‐order are calculated for short‐crested waves, oblique incident waves partially reflected on a vertical seawall, and two interacting wave trains of arbitrary wave numbers and directions.