Frequency division multiplexing based on long-period fiber grating Mach-Zehnder Interferometer(MZI) is an important way to implement fiber multiparameter sensing. The Fourier method for the composite fringes in freqency division multiplexing was investigated, with emphasis on the relationship between the value of different frequency and sum frequency in the Fourier frequency spectra and the structral parameters of the single grating in fiber MZI and then, an effect method for depressing the different and sum frequencies was proposed. The results show that the singal to noice ratio can be effectively improved by properly selecting the grating structual parameters to reduce the fringe contrast at central wavelength to a certain extend, which improves the effectiveness of filtering in freqency domain.After adjustment and optimization, the singal noice ratio of the frequency spectrum is doubled comparing to the original value. A comparison between the cosine curves of recovered phases and the orignal fringes confirms that the tuned frequency spectra remain sufficient phase information that characterize the original fringes. The spectrum optimization method developed in this paper can provide theoretical and technical guidance for multiparameter sensing based on fiber grating MZI and freqency division multiplexing.