In order to analyze the slow light effect in semiconductor optical amplifier (SOA), a theoretical model based on the slow light phenomenon induced by the coherent population oscillation effect in SOA is constructed. The effects of current modulation frequency, modulation current, direct current, linewidth enhancement factor, phase shift and relative phase of modulation current on phase delay in SOA are analyzed. The analysis results indicate that the slow light effect can be controlled by the magnitude of the modulating current and the modulating frequency. When the input direct current is less than 200 mA, the effect on controlling slow light in SOA is not obvious. Compared with the transparent current, the input direct current is larger or smaller to obtain fast light and slow light respectively. When the linewidth enhancement factor is not zero, the sideband signal light changes from fast light to slow light. It is always slow light when phase shift ψ = 0° or 90° and it is always fast light when phase shift ψ = 180°. Changing the relative phase of the modulating current enables the signal to be shifted between slow and fast light.