The residual amplitude modulation (RAM) induced by the polarized state changes of laser light in frequency modulation (FM) spectroscopy limits its application in the field of trace gas detection. The process is analyzed theoretically. The expression of the FM spectroscopic lineshape which contains the RAM is obtained. The expression of FM spectral lineshape is given when the RAM is restrained by N.C.Wong and J.L.Hall (W-H) method. The spectrum profile which contains the RAM is got by the measurement of the acetylene gases in the experiment. Then the W-H method is used to restrain the RAM and the optimized spectral lineshape is obtained. Finally, the results of the measured lineshape are fitted based on the theoretical method and the value difference between the two signals is less than 4% compared with the signal peak value.