Wave energy is attractive for its generous, sustainable and clean, the combination of floating breakwater (FB) and wave energy converter (WEC) is an economical approach to capture wave energy and attenuate waves. The conventional hybrid WEC-FB system is ineffective for low-frequency waves. To overcome this shortcoming, this paper proposed a novel WEC-FB with nonlinear stiffness mechanism to improve its wave attenuation and power capture performance. A hybrid semi-analytical nonlinear frequency-domain approach including the eigenfunction expansion matching method (EEMM) and multi-harmonic balance method (MHBM) is proposed to solve the nonlinear waves-structures interaction problem. The performance of the nonlinear WEC-FB is demonstrated by comparing with conventional linear counterpart, and the underlying reason for the effect of nonlinear mechanism is explored. The phase control mechanism for improving low frequency performance of wave elimination and energy capture is revealed by using the analytical method. This study shows that the introduction of the nonlinear mechanism can both improve the wave attenuation and energy absorption performance, especially in the low-frequency wave region.