对波荡器位相误差对自由电子激光小信号增益的影响进行了分析讨论。对低增益情况解析地给出了波荡器位相误差引起的增益降低因子。结果表明 :与自发辐射类似增益的降低与位相误差的方差成简单的指数关系 ,位相误差的线性变化部分引起最大增益的位移 ,还表明波荡器位相误差存在时Madey定理仍然成立。对高增益情况也给出了波荡器位相误差引起的增益降低因子。 The effects of the phase error of the undulator on the small signal gain of the free electron laser are analyzed and discussed. The gain reduction factor caused by the phase error of the undulator is analytically given for the low gain case. The results show that the similar gain-reduction and phase error variance of spontaneous emission are simply exponential. The linear variation of phase error causes the displacement of maximum gain, and the Madey’s theorem still holds when the phase error of undulator exists. For high gain conditions, the gain reduction factor due to the phase error of the undulator is also given.