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 timeτ_1 of the additive colored noise,τ_2 of the multiplicative colored noise,and the effect of the cross-correlation timeτ_0 between the two noises on C(s)are discussed by numerical calculation.For the case of positive correlation(λ> 0),it is found that when a_0 > 0 the normalized intensity correlation function C(s)increases with the increase of To orτ_2,and with value ofτ_0 orτ_2 becoming larger,C(s) comes to saturation.With increasing the self-correlation timeτ_1 of the additive noise,a minimum and a maximum will appear on curve of C(s)as a_0 > 0.If a_0 < 0,C(s)decreases with the increase ofτ_0,τ_1, andτ_2. Considering a single-mode laser system with cross-correlated additive additive colored noise and multiplicative colored noise, we study the effects of correlation among noises on the normalized intensity correlation function C (s) is derived by means of the projection operator method. These effects of the self-correlation timeτ_1 of the additive colored noise, τ_2 of the multiplicative colored noise, and the effect of the cross-correlation time τ_0 between the two noises on C (s) are discussed by numerical calculation. For the case the normalized intensity correlation function C (s) increases with the increase of To orττ_2, and with value of τ_0 or τ_2 becomes larger, C (s) comes to saturation. With increasing the self-correlation timeτ_1 of the additive noise, a minimum and a maximum will appear on the curve of C (s) as a_0> 0.If a_0 <0, C (s) decreases with the increase ofτ_0, τ_1, andτ_2.