A frequency response measuring system of semiconductor optical amplifiers based on direct-subtracting method is proposed according to the definition of scattering parameters of optoelectronic devices. By subtracting the frequency response of laser-photodetector system, the frequency response of an semiconductor optical amplifier its own can be obtained. With this system an InGaAsP traveling-wave semiconductor optical amplifier is measured under different input optical powers and different bias currents, and the frequency response curves are calculated. These curves indicate the gain saturation effect and the noise characters of the semiconductor optical amplifier. Moreover, it is shown that the signal gain of lower frequencies is less than that of higher frequencies. The reason is the carrier lifetime of semiconductor optical amplifier is limited. Lower-frequency signals have longer period to deplete carriers continuously, therefore the number of carriers cannot resume in time.