By using the linear approximation method, the intensity correlation time is studied for gain-noise model of a single-mode laser driven by white pump noise and white quantum noise with colored cross-correlation. It is detected that the noise correlation coefficient has a great effect on the curves of the intensity correlation time upon the noise intensities. When the noise correlation coefficient is positive, there exist maximum (i.e., resonance) in the curves of the intensity correlation time upon the noise intensities. When the noise correlation coefficient is negative, there exist minimum (i.e., suppression) in the curves of the intensity correlation time upon the noise intensities. And when the noise correlation coefficient is zero, there are neither maximum nor minimum in the curves, the intensity correlation time increases monotonously with the increasing of the noise intensities. Furthermore, the effect of the cross-correlation time, the attenuation coefficient and the signal frequency on the intensity