By means of an extended colored-noise approximation，we investigated the effects of asymmetry of the potential and noises on the mean first-passage time T+（xs1→xs2） and T-（xs2→xs1） in two opposite directions in an asymmetric bistable system （here xs1 and xs2 are stable points of the asymmetric bistable system）. Numerical results show that T+（xs1→xs2） decreases with increasing of τ1 （the correlation time of multiplicative noise） and τ2 （the correlation time of additive noise）. T-（xs2→xs1） increases with increasing of τ1 and τ2. The curves of T+（xs1→xs2） versus λ and T-（xs2→xs1） versus λ are single-peaked. T+（xs1→xs2） will increase when r increases，but T-（xs2→xs1） will decrease when r increases.