By combining shooting method with Runge-Kutta method for solving differential coupling equations of backward-pumped fiber Raman amplifier (FRA),the effects of fiber length,initial signal power,initial pump power,fiber efficient area,Raman gain coefficient,and fiber loss of signal and pump on gain of FRA have been detailedly investigated. Finally,several ways are suggested to improve the gain of backward-pumped FRA. Accurate and reasonable results have been gotten,and are helpful to the study of FRA.