Abstract: By reducing the lattice symmetry of the square lattice, two−dimensional photonic crystal with a rectangular lattice of circular dielectric rods was employed to obtaining the complete photonic band gap (CPBG) under the condition of low refractive index. Plane wave expansion method was employed to study the CPBG of two−dimensional photonic crystal. The result reveals that both square lattice and rectangular lattice favor TM PBGs, but the reduction of lattice symmetry can produce an increase in the number of PBG and a broadening of PBG width for TE modes, which is conductive to obtaining CPBG under the condition of low refractive index for the rectangular lattice: the CPBG is observed when the refractive index of the dielectric materials is larger than 2.0.