It is of great practical significance to make use of the inverse magnetostrictive effect of Galfenol and adjust the band gaps of its phononic crystal(PC) through the shunt element to achieve effective vibration reduction. Based on the magnetostrictive constitutive equations, Armstrong model, Faraday law, transfer matrix method and Bloch theorem, the effective elastic modulus expression of Galfenol with shunt circuit is derived and the vibration model of the PC is established. The comparisons between the calculated and measured results show that the proposed model can provide a reasonable data trend of the effective elastic modulus with the change of frequency and shunt capacitance, and can predict the nonlinear behaviors of Galfenol parameters with the change of the stress. The variation of the peak value of the Bragg band gap(BBG) attenuation constant and the cutoff frequency of the PC under open circuit with stress is analyzed, and the optimal operating point for vibration reduction is determined. The characteristics of BBG, resonance band gap(RBG) and resonance common band gap(RCBG) of the PC under different shunt capacitance and stress are analyzed. The results show that smaller shunt capacitance, larger magnetomechanical coupled factor and larger inductance can significantly improve the vibration reduction performances of the PC.