By comparing the energy band of 2D photonic crystal with square and triangular lattice, the 2D triangular lattice for the study is selected. The photonic band gap (PBG) can be formed by the periodicity of the permittivity in the photonic crystal, and then the movement of the photon is controlled. The single-line-defect photonic crystal waveguide is proposed, the effect of the energy band structure and dispersion relation with the line defect on the group velocity is analyzed, and the group velocity dispersion (GVD) of the effective slow-light region is at 105 ~ 106. To realize the dynamic adjustment of group velocity, the permittivity and the lattice radius are changed, the group velocity can be adjusted to below 0.1c. The simulation shows that the fundamental factors impacting the group velocity is the changed frequency of the defect band.