Abstract: Band gap characteristics of the photonic crystals with triangular lattice of air cylinders and triangular lattice of dielectric cubes were comparatively studied by means of plane wave method. 2D photonic crystal with triangular lattice of air cubes was put forward and the influence of dielectric constant on the band gap width was analyzed. The results show that the band gap width of photonic crystal with triangular lattice of air cylinders is much wider than that of photonic crystal with triangular lattice of dielectric cubes when the photonic crystals are made of the same material. For photonic crystal with triangular lattice of air cubes, theoretical calculations show that two complete photonic band gaps occur and the relative dielectric constant more than 12.0 for the appearance of two gaps. The two band gap width reaches its maximal value when the relative dielectric constant is 19.0.