We introduced two correlated Gaussian multiplicative white noises into the Logistic growth model for an anti-tumor system subject to immune surveillance. Considering various active thresholds to initiate the immunity of the anti-tumor system, we made numerical simulations to investigate how the intensity λ of two correlated white noises influences the immune effect of an anti-tumor system. Our numerical results reveal that the correlation intensity λ has an optimal value, at which the anti-tumor system will achieve functionally the best immunity.