In this paper,the effects of colored correlations and asymmetry of the potential on the mean first-passage time(MFPT) are investigated for an asymmetric bistable system driven by multiplicative noise and additive noise.Numerical results show that the intensities of multiplicative and additive noises and the cross-correlation time τ affect the MFPT in the same way,the coupling strength λ and asymmetry r of the potential affected the MFPT in the same way.The increase of τ enhances the escape rate,while increase of λ reduces the escape rate.