The effect of quantum colored noise on single-mode laser gain model is studied. The analytical expressions of the time-dependent moments, the correlation function and power spectrum of the laser intensity are derived by means of linear approximation method. It is shown that the statistical properties of the laser intensity are mainly decided by quantum colored noise when the laser is operating near the threshold. The conclution is that the initial plateau of the intensity correlation function observed by experiment is due to the “color” of the noises and predict that the intensity variance will also exhibit initial plateau.