With the rapid development of all-optical networks, fast and slow light technology has gained widespread attention. In this paper, a theoretical model of assist light injection into semiconductor optical amplifier (SOA) was constructed to study the fast and slow light effect. The effects of the gain coefficient and the magnitude of DC current, modulation current, modulation frequency and phase shift on the phase delay with and without the injection of assist light were compared. The simulation results show that the output signal light changes from slow light to fast light under the injection of assist light, and the stronger the assist light power, the more obvious the effect. Meanwhile, it can be observed that after the injection of the assist light signal, the larger the DC current, the larger the phase delay. On the contrary, the larger the modulation current, modulation frequency, phase shift and gain coefficient, the smaller the phase delay.