Plane wave expansion method is applied to simulate the bandgap of two-dimensional photonic crystals made of a triangular lattice of dielectric rods(circular,hexagon,square cross sections) in air. Moreover, the effect on band gap of a triangular lattice of square dielectric rods in air is discussed as a function of the rotation angle, the refractive index and the filling fraction, respectively. In the low frequency region, the maximum complete photonic band gap appears when the rotation angle equals 17 degrees. the maximum complete photonic band gap can be attained steadily as the refractive index changes continuously. In the high frequency region, the maximum complete photonic band gap appears when the rotation angle equals 30 degrees. The complete photonic band gap is observed when the refractive index is greater than 2.2. The width of complete photonic band gap reaches the maximum when the dielectric refractive index is equal to 2.6.