By adding modulation wave to the equation of the laser intensity in the gain-noise model of the single-mode laser, we use the linear approximation method to calculate the power spectrum and signal-to-noise ratio(SNR) of the laser intensity, which is driven by two color noises correlated in the form of exponential function. The result shows that the correlated time and the correlated strength between the noises have great effect on the stochastic resonance(SR), and the variations of SNR with the frequency of the carrier signal ω and the modulator signal Ω are quite different from the curve of variation of white noise.