This article proposes a non-linear vibro-impact mechanism, integrated inside a semi-submerged cylindrical buoy to form a self-contained and self-referenced vibro-impact wave energy converter (VIWEC), for performance enhancement. A non-linear mathematical model of the VIWEC is derived, considering linear wave-buoy interaction and non-linear vibro-impact mechanics. Numerical simulations are conducted to investigate the influence of the vibro-impact mechanism on the VIWEC's dynamics and performance. Numerical results conclude that the VIWEC is characterised by a band-pass frequency response and inherently decoupled from ocean waves of low frequencies, indicating high survivability under extreme sea states. The vibro-impact mechanism can also broaden the VIWEC's power capture bandwidth and limit the VIWEC's motion within its physical constraint. On the other hand, the VIWEC's dynamics are sensitive to design parameters, and an improper design may lead to rich and complex non-linear dynamics of the VIWEC, e.g. chaos and multi-stability. The proposed non-linear model can provide a platform for design optimisation and control development of the VIWEC.