Abstract: Under considering the energy spread,emittance of the electron beam and the random field error of the wiggler,we resolve the FEL’s self-consist equations in low gain region. Then applying the condition of stable radiation field,we obtain the threshold relationship of FEL’s parameters such as energy spread,emittance, field error and current, and so on. Finally,these experimental parameters of four typical small-signal FEL are used to testify the result obtained in the article.