Investigated are the effects of the cross-correlation time τ or the self-correlation times τ1 and τ2 on the relaxation time T of an optical bistable system using the Mei's method(Mei D C, Xie C W, Zhang L 2003 Phys. Rev. E 68 051102). It is found that the relaxation time T increases with the increase of the cross-correlation time τ between the two noises or the self-correlation time τ1 of the multiplicative noise, and that a one-peak structure appears on the T－τ2 plot. T increases with the increase of correlation intensity λ but decreases with the increase of multiplicative noise intensity Q.