Considering a single-mode laser system with cross-correlated additive colored noise and multiplicative colored noise, we study the effects of correlation among noises on the normalized intensity correlation function C(s). C(s) is derived by means of the projection operator method. The effects of the self-correlation time \tau1 of the additive colored noise, \tau2 of the multiplicative colored noise, and the effect of the cross-correlation time \tau0 between the two noises on C(s) are discussed b