A single-mode laser model with cross-correlated additive and multiplicative noise terms is considered, and the effects of correlation between noises on the relaxation time and the intensity correlation function are studied. Using the projection operator method and taking into account the effects of the memory kernels of the intensity correlation function, the analytic expressions for the relaxation time and the correlation function are derived. Based on numerical computations, it is found that the self-correlation time and the cross-correlation time have the same effects on the single-mode laser system.