Defect modes will emerge in the emission spectrum as a defect is introduced in a photonic crystal, and such modes can be amplified to produce laser radiations. Based on the model that couples Maxwell's equations with the rate equations of electronic population, the spatial distribution and spectrum characteristics of the laser modes in a single-defect active photonic crystal are investigated by the finite-difference time-domain method, as well as the amplification of defect modes. The influences of the number of crystal periods and the thickness of the defect layer on amplification of defect modes are analyzed. The results show that the spectral property, resonance and radiation frequency, and spatial profile of defect mode depend directly on the medium parameters such as the number of crystal periods and the thickness of defect layer, which further influences the radiation threshold and saturation. The radiation threshold decreases and the saturated output increases when the number of crystal periods increases. Such a trend becomes weak when the number of the crystal periods is large enough and thus there exists an effective number for the crystal periods in the system.