Purpose <p>The vibration absorber based on nonlinear energy sink (NES) and piezoelectric effect can convert the energy absorbed by NES from the primary structure into electrical energy through piezoelectric effect to achieve the dual efficacy of vibration suppression and vibration energy harvesting for the primary structure.</p> Methods <p>The electromechanical-coupled governing equations of the primary structure coupled with the NES-piezoelectric system are derived based on Newton’s second law and Kirchhoff’s voltage law. The approximate solution is derived by the complexification-averaging method.</p> Results <p>The instability boundary and output response are numerically and analytically explored. The Hopf bifurcation phenomenon of the mass, damping, cubic stiffness of NES and the external resistance of the energy harvesting device on the output response of the system are investigated. The motion forms in the bifurcation region are also discussed through time history curves, spectrograms, phase-trajectory plots and Poincaré cross-sections.</p> Conclusion <p>The results indicate that variations in the parameters of the NES and the external circuit can lead to Hopf bifurcations in the output response of the system. In the unstable region determined by Hopf bifurcation, the response of the system may exhibit strongly modulated and chaotic responses that are favorable for vibration suppression and vibration energy harvesting.</p>