The propagation and switching of fundamental solitons in three-core fiber nonlinear directional coupler with three cores in an equilateral-triangle arrangement have been investigated with two methods. Firstly, by using variational method, we obtained the　equation of transmission coefficient with respect to distance. Secondly, we used the split-step Fourier method (SSFM) to solve the nonlinear Schrdinger equations. The results of both variational method and SSFM indicate that the energy of optical pulses transfer periodically between the three cores and have sharp switching characteristics when the first order intermodal dispersion coefficient is small. Otherwise, the periodicity of the coupling transmission characteristics of optical solitons in fiber coupler and the sharpness of switching are destroyed. The second order intermodal dispersion coefficient and initiative chirp reduce the coupling length, shorten the periods of the energy transfer of optical pulses between the three cores, and increase the threshold switching power. Though the cross phase modulation coefficient has weaker impact on transmission characteristics, it increases the threshold switching power of couplers.