We proposed a novel method to analyze the propagation of sub-picosecond optical pulses through semiconductor optical amplifiers(SOA), fully considering spectral dispersion of ultrashort pulses. A reasonable model is established via sampling the pulses simultaneously in time domain and frequency domain. Based on the established model, we observed an evident shift of the pulse spectrum, which agrees well with the experiment results in literature. Further, the relationship is discussed respectively between the value of shift and several external conditions, including wavelength, energy, width of the pulse, length of SOA and injected current. Gain suppression induced by ultrafast nonlinearities including carrier heating, spectral hole burning and two-photon absorption is described in detail, employing two-beam configuration. The simulated results give good guidance to the improvement of ultrafast dynamic characteristics of SOAs.