The effects of correlation between additive and multiplicative noises on the symmetry of an asymmetric bistable system are investigated. The steady-state probability distribution function of the system was calculated by using analytical and numerical methods. Results indicate that i) for the case of positive correlation between noises, as the correlation strength between additive and multiplicative noises, λ, increases, the symmetry of the system is restored; ii) for the case of negative correlation between noises, as the absolute value of λ increases, the symmetry of the system is destroyed; and iii) the analytic prediction agrees well with the stochastic simulation result.