By means of the linear approximation method, we calculate the intensity correlation time T of the single-mode laser system with the cross-correlation intensity λ between noises modulated by time period. The results show that whether λ=0, λ>0 or λ<0, the intensity correlation time T increases monotonously with the quantum noise intensity D and pump noise intensity Q, and tends to saturation finally (T=1). The evolution of the intensity correlation time T with pump noise intensity Q appears a restraint for λ<0, i.e. a mininum. When λ=0, the intensity correlation time T does not change with the time period modulation frequency Ωλ. When λ>0 and λ<0, the evolution of the intensity correlation time T with Ωλ presents high-frequency oscillation for smaller Ωλ. Increasing Ωλ, the oscillation frequency becomes small and amplitude decreases. Finally, the intensity correlation time T is consistent with that of λ=0.