The band structure and the optical transmission properties of the two-dimensional photonic crystal with complex dielectric constant, especially discussing on the case of negative imaginary part, are analyzed numerically with the plane-wave expansion method. The results show that the spontaneous emission of special light frequency that is in the range of photonic band gap is effectively restrained. A large enhancement of stimulated emission appears at the photonic band edges where the group velocity is small if the photonic crystal is with a little impurity atoms that have population inversion. This phenomenon will happen even if the dielectric constant difference between two dielectrics is very small. Generally, there is a small group velocity near the photonic band gap. Because the threshold of emitting laser is proportional to the square of group velocity, the lasing threshold decreases with a decrease in the group velocity. This might be used either to realize lasing operation near zero thresholds, or to supply a beneficial reference for fabricating optical amplification device.