By means of the linear approximation, we investigate the power spectrum and signal-to-noise ratio of the laser intensity for the gain-noise model of the single-mode laser with the noise correlation intensity λ modulated by the time period. Effects of the noise intensity D and Q, the noise correlation intensity λ, the period modulation frequency Ωλ and the input signal frequency Ω on the signal-to-noise ratio R are discussed. Some novel phenomena are found.