By means of the three-dimensional (3D) finite-difference time domain (FDTD) method, we have investigated in detail the optical properties of a two-dimensional photonic crystal (PC) surface-emitting laser having a square-lattice structure. The 3D-FDTD calculation is carried out for the finite size PC slab structure. The device is based on band-edge resonance, and plural band edges are present at the corresponding band edge point. For these band edges, we calculate the mode profile in the PC slab, far field pattern (FFP) and polarization mode of the surface-emitted component, and photon lifetime. FFPs are shown to be influenced by the finiteness of the structure. Quality (Q) factor, which is a dimensionless quantity representing photon lifetime, is introduced. The out-plane radiation loss in the direction normal to the PC plane greatly influences the total Q factor of resonant mode and is closely related with the band structure. As a result, Q factors clearly differ among these band edges. These results suggest that these band edges include resonant modes that are easy to lase and resonant modes that are difficult to lase.