A state equation of absorptive optical bistable system driven by colored multiplicative noise was built by using the unified colored noise approximation. The results were discussed and compared with the system with white noise. The results show that, when the multiplicative noise and the additive noise are in positive correlation, the area of optical bistability broadens outstandingly, that also is the hysteresis cycle width is broaden with the increasing of self-correlation time τ; whereas when the multiplicative noise and additive noise are in negative correlation, and only when the multiplicative noise strength is weak, the change of self-correlation time τ can induce the change of the area of optical bistability; when the self-correlation time τ of multiplicative noise is equal zero, the model of the system with colored noise falls back to the model of the system with white noise.