A two-dimensional photonic crystal consisting of two square arrays of square dielectric columns with different sizes in air is proposed and investigated theoretically. For the proposed structure, Maxwell’s equations are Fourier transformed rigorously, and a plane-wave expansion method with fast convergence is then formulated. With this method, the band structure of the photonic crystal is numerically analyzed carefully. It is shown that compared with the related structure with a single square lattice, the absolute band gap of the proposed structure is remarkably increased after optimizing the geometric parameters, owing to the decrease of the structural symmetries.