In order to analyze and accurately predict the performance of semiconductor optical amplifiers, an effective mathematical model of InP-InGaAsP uniformly buried semiconductor optical amplifier was established. Considering the relationship between spontaneous and stimulated radiation, the effects of bias current and input power on gain and noise index were analyzed by real-time simulation. The results show that, when the bias current is 120mA and the input power is -10dBm, semiconductor optical amplifier has the best performance. The model can provide some reference for the design of semiconductor optical amplifier.