Considering an optical bistable system with cross-correlated additive white noise and multiplicative colored noise, we study the effects of correlation between the noises on the correlation function C(s) using the unified colored noise approximation and the Stratonovich decoupling ansatz formalism. The effects of the self-correlation time \tau of the multiplicative colored noise and the correlation intensity \lambda between the two noises are studied with numerical calculation. It is found that C(s) increases with the increase of the self-correlation time \tau, but decreases with the increase of the correlation intensity \lambda. At large value of \tau, there is almost no change for C(s) when  changes.