In order to solve the three problems of terahertz optical asymmetric demultiplexer-cross phase modulation effect based all-optical exclusive-OR gate, which are that the strict demand of synchronization; cannot be applied in the situation of not return to zero signal input; the speed of exclusive-OR operation is limited by carrier recovery speed of semiconductor optical amplifier. An all-optical exclusive-OR gate was proposed which utilizes the structure of terahertz optical asymmetric demultiplexer and is based on four wave mixing effect, because of based on four wave mixing, this exclusive-OR gate can radically solve the mentioned three problems of terahertz optical asymmetric demultiplexer-cross phase modulation based exclusive-OR gate. This paper illustrates the principle of this exclusive-OR gate through theoretic analyse, and realizes the exclusive-OR operation for the input of 40 Gbps, return to zero signal; 80 Gbps, return to zero signal; 10 Gbps, not return to zero signal. The Q factor and bit error rate of exclusive-OR operation for above three kinds of input are 11.7, 2.4×10-18；8, 1.1×10-10；22, 1.3×10-40. And then, we analyse the influence on the quality of exclusive-OR output signal which is generated by change of parameter of main elements of terahertz optical asymmetric demultiplexer and temperature and dispersion effect. The feasibility and effectiveness of this exclusive-OR gate for solving the three problems of terahertz optical asymmetric demultiplexer-cross phase modulation based all-optical exclusive-OR gate are verified by theoretic analyse and simulation.