According to the research of rectangular photonic crystal slab, an L3 square air holes photonic crystal cavity is proposed. The Q factors, mode volumes, and resonant frequencies of L3 square air holes photonic crystal cavities with different side lengths are discussed using finite difference time domain (FDTD) method. Based on the results, an L3 square air holes photonic crystal cavity is proposed and a fairly high Q value of 27719 is obtained, with the mode volume of 0.4361(λ/n)3 and the resonant wavelength at 1543 nm. The Purcell factor of the L3 square air holes photonic crystal cavity is as high as 4767.