The intensity correlation time T is studied for gain-noise model of a single-mode laser driven by colored pump noise and colored quantum noise with colored cross-correlation. By using the linear approximation method,we detect that there exist maximum(i.e. resonance)in the T-D and T-I₀ curves when the noise correlation coefficien λis positive;and there exist minimum(i.e. suppression)in the T-D curves and exist one minimum and one maximum in the T-I₀ curves when λ is negative. When λ is zero,The intensity correlation time Tincreases monotonously with the increasing of the quantum noise intensity D and steady-state intensity I₀. However,no matter what the value λ is,the intensity correlation time T decreases monotonously with the increasing of the periodic signal amplitude A and the attenuation coefficient γ. Furthermore,we analyze the effect of signal frequency,Ω. and the cross-correlation time ₃ on the intensity correlation time T,find that has little effect on the T-D,T-I₀,T-A and T-γ curves,and ₃ has great effects on the T-D,T-I₀ and T-A curves but has little effect on the T-γ curves.