The phenomenon of vibrational resonance (VR) in an overdamped system with a sextic double-well potential under the excitation of two different periodic signals is investigated. The approximate analytical expression of the resonance amplitude.. at the low-frequency omega is obtained. The VR is observed, and the values of.. (the amplitude of the high-frequency signal) and Omega (the frequency of the high-frequency signal) at which VR occurs are determined. Moreover, the relationship between B and Omega is revealed. The theoretical predictions are found to be in good agreement with the numerical results.