Optical fiber amplifier is an indispensable optical device in distributed sensing system to realize ultra-long-distance, ultra-low loss transmission. The noise characteristics of amplifier have a vital impact on the overall performance of the distributed sensing system. In the differential interference distributed sensing system, the broadband spectrum light source must be used, and the detection terminal must also use the wide spectrum detection, so it was of great significance to study the noise of EDFA in the broadband spectrum distributed sensing system for the improvement of the overall performance of the sensing system. The response relation of EDFA gain to the wavelength and power of the broadband spectrum light source was studied in this paper, and the gain response curve that can describe this relation was obtained. Based on this curve, an estimation method that can characterize the noise of the broadband spectrum light source amplified by EDFA was proposed, and the noise rule of EDFA amplified broadband spectrum light source was summarized.