Ten types of two-dimensional Archimedean lattices were classified by square-like lattices and triangle-like lattices.Then the properties of photonic band gaps in the photonic crystals were studied by the plane wave expansion method.The effect of the normalized radius on the band gaps is discussed,and the band gap widths of above photonic crystals of lower frequency were compared.The numerical results show that the photonic crystals with square-like lattices and triangle-like lattices have some isotropic band gaps and lower frequency band gaps for the TM modes,the complete band gaps for the TE and TM modes were produced easily.The lower boundary values of first band gap for the TM modes are analyzed is minimal for the (32.4.3.4) and (3.6.3.6) lattices by analysis.The maximum values of those band gaps for the TM modes in the square-like lattices and triangle-like lattices are obtained if choosing an approriate normalized radius 0.2 and 0.26,and the typical photonic crystal with compound lattice has complete band gap.The research can pave a way in the design of new optical devices.