Based on coupled nonlinear Schrdinger equation (NLSE) and the split-step Fourier method (SSFM), a numerical investigation of the propagation and the switching of fundamental solitons in two-core fiber nonlinear directional coupler (NLDC) with high order coupling dispersion coefficient is present. In this model, the first coupling dispersion is similar to the group velocity mismatch. The second coupling dispersion is similar to the group velocity dispersion (GVD), and it leads to mutual modulation for the other channel. Optical pulses propagate periodically inside fiber coupler and NLDC have sharp switching characteristics when the first order coupling dispersion coefficient is smaller, but the periodicity of the coupling transmission of optical solitons and the sharpness of switching were destroyed by the increase of the first order coupling dispersion coefficient, so optical pulses breakup in the propagation. The second order coupling dispersion coefficient reduce the coupling length, and increase the switching threshold power, as well as make switching characteristics become sharper.