A widely tunable regenerative terahertz parametric amplifier is proposed based on degenerate four-wave mixing in an asynchronously pumped highly nonlinear medium. To enhance the Kerr nonlinearity, a hybrid structure of cyclic olefin co/polymer (COC/P) TOPAS integrated by a graphene oxide film is utilized as the gain medium and embedded into a cavity. A low-power terahertz seed wave is injected inside the cavity and sequentially pumped by four asynchronous coupled beams of identical powers. Our results reveal that the output power, the tuning frequency range and the power conversion efficiency of terahertz waves could be considerably improved in the proposed design. Terahertz waves with maximum peak power of 641 W, the accumulated conversion efficiency of 3.8% and amplification gain of 320.5 are obtained at a frequency of 9.61 THz, which could be tuned over a range of 1.17 - 19.736 THz.