Abstract: The transient properties of a bistable system driven by colored cross-correlated noises is studied.According to Novikov theorem and Fox′ approach,we derive the approximative Fokker-Planck equation.The analytic expression of the mean first-passage times(MFPT)in two opposite directions is derived by the steepest-descent approximation,i.e.,T+(from the left well to the right) and T-(from the right well to the left). From numerical computations we find the following: ① The colored correlation between the additive and the multiplicative noises makes the system escape easier in one direction and more difficult in the other direction;② The correlation time τ causes the suppression of escape rate from the left well to the right well to become inapparent for the case of the positive correlation between noises(λ0);and τ causes the suppression of escape rate from the right well to the left well to become inapparent for the case of the negative correlation between noises(λ0);and the colored correlation among noises play opposing roles on the MFPTin any direction for λ0 and for λ0.