Abstract: The Four Wave Mixing(FWM) of the quantum dots semiconductor optical amplifiers(QD-SOA) was investigated by using the finite differential method based on the transitions between energy levels. The effects of the parameters on the efficiency of FWM were analyzed by simulation. The efficiency of FWM increased with the increase of the power of pump light, the length of QD-SOA and the injected current. The efficiency of FWM decreased with the increase of the power of the probe light and wavelength space. The exclusive-OR(XOR) logic of differential phase-shift keying signals was realized based on the FWM effect and the time domain and frequency domain results of the XOR logic were got by simulation. The XOR logics at position with different wavelengths were realized simultaneously. The XOR logic of 32-bit sequence was investigated and the XOR result and the eye diagram were achieved.