We study the realization of dual-bistability flip-flop converter in cavity and parametrically amplified four-wave mixing (FWM) process at a four-level cavity atomic system. Using the effect of nonreciprocity optical dual-bistability, we can obtain different output multi-mode states of probe transmission signal and FWM signal. We find the channel equalization ratio and optical contrast between multi-mode states is related to the degree of dual-bistability. Besides, the degree of dual-bistability can be controlled by the input parameters (frequency detuning and powers of the dressing beams). More, using electro-optical modulator and acoustic optical modulator to modulate the powers and frequency detuning, respectively, we can realize the fast conversion between different output states. And the switch speed of this flip-flop converter is about 16 ns. These outcomes may provide foundation for the development of all-optical devices and quantum information processing.