The single-partiol? model is used to explain the working principle of free-eloofcroa laser amplifier. After linearizing the motion equation of electron,we got the small-signal gain. The results show that the electron beam has suitable initial velocity distribution, the initial phases of the static periodic magnetic field and incidont oleotromagnetio wave have definite relation, the syohronization requirement between electrons and wave and the cyclotron rosonace oondition are satisfied. The electrons can transfer their energy to the wave efficiently and oonstanily so that laser amplitioation can be achievod.