Vibration energy harvesting and vibration isolation and are conflict in most existing works. As for suspension systems, vibration isolation is always considered as the main goal. In this case, the efficiency of vibration energy harvesting is sacrificed to achieve a trade-off optimization, so it is urgent to reveal the relationship between vibration energy harvesting and vibration isolation. In this paper, a one-degree-of-freedom (1-DOF) simultaneous vibration isolation and energy harvesting (SVIEH) system is investigated by using quasi-zero stiffness (QZS) and its electromechanical coupling equation is derived. The output power and the force transmissibility are selected to evaluate the performances vibration energy harvesting and vibration isolation, respectively. Then the coupling mechanism between the two performance indices is clarified by numerical analysis and the key parameters for possible de-coupling are revealed, including damping ratio, electromagnetic coupling coefficient, load resistance and external excitation.