Gain saturation is a significant phenomenon of fiber Raman amplifiers (FRAs). Gain figures versus signal power are well explained. For the small signal, the coupled ordinary differential equations are used, and for the large signal, the Raman gain coefficient is modified. It is shown that the saturation power of FRAs decreases with the pump power, and gain saturation is easier to occur in the forward pump scheme than in the backward pump scheme. These phenomena are well explained by the stimulated Brillouin scattering (SBS) effect. This research provides a guide to the fabrication of practical FRAs.