A theoretical model of semiconductor optical amplifier (SOA) is presented with carrier density pulsation (CDP)，free-carrier absorption (FCA)，stimulated emission (SE)，two-photon absorption (TPA)，spectral hole burning (SHB) and ultrafast nonlinear refraction (UNR) taken into account. The model is proved by comparing with the reported experimental results. The prevailing SOA model is revised. The influences of FCA and TPA processes on ultrashort strong optical pulses are analysed. When the strong optical pulse with several-picosecond pulsewidth is injected into the SOA operating under the transparency current，the intensity characteristics of the optical pulse are mainly influenced by TPA and FCA. As a result of taking the FCA effect into account，the intensity transmission characteristics of 200fs optical pulses obtained by the new model basically agree with the experimental results. It broadens the applicability of the model.