By means of linear approximation method, the intensity correlation function, correlation time and power spectrum for the gain-noise model of a single-mode laser driven by correlated noises are derived. Effects of mutual-correlation-time and self-correlation-time for the noise on the above-mentioned properties of the laser are analysed and discussed. It is found that, in a single-mode laser system driven by correlated noises, effects of two noise-correlation-time on statistical properties of the laser are quite different. Some novel phenomena are obtained.