A triangular photonic crystal is designed theoretically. An analysis on the transmission properties of the transverse electric mode (TE mode) in two dimensional (2D) photonic crystal with triangular lattice is presented based on the finite difference time domain technique. The frequency spectrum is extracted from the simulated electromagnetic field data by Fourier transform. By analyzing the phase of each spectral component, the equivalent refractive index of a photonic crystal is calculated. the results show the different relationship between the spatial frequency and phase velocity. For the frequency of positive refraction, the phase velocity and energy are in the same direction. On the contrary, For the frequency of positive refraction, the phase velocity and energy are in the opposite direction. The result might provide a solid theoretical basis in the inquisition of photonic crystal physical mechanism.