By using the linear approximation method,the intensity correlation function and the intensity correlationtime are calculated in a gain-noise model of a single-mode laser driven by colored cross-correlated pump noise andquantum noise,each of which is colored.We detect that,when the cross-correlation between both noises is negative,thebehavior of the intensity correlation function C(t) versus time t,in addition to decreasing monotonously,also exhibitsseveral other cases,such as one maximum,one minimum,and two extrema (one maximum and one minimum),i.e.,someparameters of the noises can greatly change the dependence of the intensity correlation function upon time.Moreover,we find that there is a minimum T_(min) in the curve of the intensity correlation time versus the pump noise intensity,andthe depth and position of T_(min) strongly depend on the quantum noise self-correlation time _2 and cross-correlation time_3. By using the linear approximation method, the intensity correlation function and the intensity correlation time are calculated in a gain-noise model of a single-mode laser driven by colored cross-correlated pump noise and quantum noise, each of which is colored. We detect that, when the cross-correlation between both noises is negative, the behavior of the intensity correlation function C (t) versus time t, in addition to decreasing monotonously, also showsseveral other cases, such as one maximum, one minimum, and two extrema (one maximum and one minimum), ie, someparameters of the noises can greatly change the dependence of the intensity correlation function upon time. Moreover, we find that there is a minimum T_ (min) in the curve of the intensity correlation time versus the pump noise intensity , and the depth and position of T_ (min) strongly depend on the quantum noise self-correlation time _2 and cross-correlation time_3.