Vibration-based energy harvesting devices are prone to excessive displacement response. The effective vibration suppression is critical to the longevity and safety of energy harvesting systems. In this work, the vibration-based Piezoelectric–Electromagnetic energy harvester with nonlinear energy sink (NES-VBPEEH) is proposed to achieve the dual efficacy goals of vibration suppression and vibration energy harvesting. The electromechanical-coupled distributed governing equations are derived through Hamilton’s principle, Euler’s Bernoulli theory, Gauss’s law and Faraday’s law of electromagnetic induction. The output performances of the degradation model of the NES-VBPEEH are validated by previous work. Parameter analysis indicates that the external resistance of the piezoelectric energy harvester significantly affects the electrical damping of the system and ultimately affects the output response of the NES-VBPEEH. The external resistance and coil turns of the electromagnetic vibration energy harvester can significantly affect the output response of the NES-VBPEEH. The output power of both types of energy harvesters is maximized with respect to the resistance and the coil turns. The output response of the NES-VBPEEH exhibits certain nonlinear characteristics as the external excitation amplitude increases to a certain value. The damping and nonlinear stiffness of the NES can significantly affect the output power of the NES-VBPEEH, and appropriate parameter selection can help to achieve the dual efficacy goals of vibration suppression and vibration energy harvesting for the energy harvester.