Shunted piezoelectric patches connected to passive electric circuits can be attached to a host structure for effective attenuation of structural vibrations. The structure under consideration consists of a beam, piezoelectric patches and possibly an auxetic layer between them. In this study, a new technique is presented for enhancing the vibration suppression of structure by using an auxetic layer between the shunted piezoelectrics. First, a modification of the "current-flowing" shunt circuit for multimode vibration control is presented. Two finite element (FE) models are created to simulate the dynamic behavior of the beam. The frequency response of the compound system and the optimal values of the electric parameters are calculated by using two FE models and a comparison is provided. Finally, it is shown that the vibration reduction of the second and third eigenmodes can be enhanced, provided that an auxetic of considerable thickness is placed between the piezoelectrics and the structure.