This paper presents a micro electromagnetic vibration energy harvester (VEH) that uses complementary metal-oxide-semiconductorcompatible 3D micro-electromechanical system coils and a ferromagnetic core to improve efficiency and output power. A systematic model is proposed to describe the nonlinear electromagnetic damping coefficient and nonlinear attraction between the magnet and the ferromagnetic core. The nonlinear model agrees well with the finite element calculation results. Then, a vibration model is established by considering nonlinear stiffness and damping coefficient to obtain the dynamic characteristics and output performance of the system. Furthermore, a numerical method is conducted to systematically investigate the influence of air gap and initial magnet offset under different excitation amplitudes. The simulation results indicate that with a smaller air gap, the output power is higher. Moreover, there is an optimal initial magnet offset in relation to the air gap to maximise the output power of the system. These conclusions and analysis models can be generalised and can be used as a guidance for the designs of similar structural devices. The results also show that the structure proposed in this study can significantly enhance the energy harvesting performance compared with published data of conventional VEHs.