Plane wave expansion method is introduced to simulate the band structures of two-dimensional photonic crystals made of Archimedes A7 lattice of circular and square dielectric rod in air. The bandgaps of Archimedes A7 lattice with dielectric rods is also discussed as functions of the refractive index, filling fraction and rotation angle. The results show that the complete bandgap can be obtained when the refractive index is greater than 2.40. The width of complete bandgap reaches the maximum when the dielectric refractive index of the circular rod is equal to 2.60. For the Archimedes A7 lattice of square dielectric rod, the complete bandgap reaches the maximum when the dielectric refractive index equals 3.80. The maximum complete bandgap changes in a narrow range as the refractive index increases. When the rotation angle of the square dielectric rods changes, the maximum bandgap keeps constant for a fixed refractive index. However after the change of rotation angle, the complete bandgap appears in a large scale of the filling fraction.