A parabolic-bistable potential system driven by colored noise is studied. The exact analytical expressionsof the stationary probability distribution (SPD) and the moments of the system are derived. Furthermore, the meanfirst-passage time is calculated by the use of two approximate methods, respectively. It is found that (i) the double peaksof SPD are rubbed-down into a flat single peak with the increasing of noise intensity; (ii) a minimum occurs on the curve of the second-order moment of the system vs.noise intensity at the point DΓ=0.025;(iii)the results obtained by our approximate approach are in good agreement with the numerical calculations for either small or large correlation time Γ，while the conventional steepest descent apprximation leads to poor results.