In this paper, the vibration band gap properties of a two-dimensional square lattice are studied using the spectral element method. Before assembling the spectral equations of whole structures, the spectral stiffness matrices of the tensional and bending elements are established. The frequency responses of the lattices are calculated and compared with those obtained by the finite element method. It can be observed that the results in the spectral element method are more accurate, especially in high frequency ranges. The frequency band gap properties are analyzed based on the accurate frequency responses. The effects of the material and structure parameters on the band gap properties are investigated.