In order to analyze the threshold characteristics of forward- pumped fiber Raman amplifier (FRA), signal power distribution along a fiber for forward- pumped FRA is provided with Runge- Kutta method based on the coupling equations. Then, the theoretical expression of forward- pumped FRA′ s threshold is obtained with considering the practical factors, and the effects of these parameters on threshold of FRA are investigated detailedly. It is found that: the threshold will decrease when the initial signal power, the effective fiber length, Raman gain coefficient or the pump and signal frequency ratio increase, and the threshold will increase when the fiber efficient area increases.