Fiber optic acoustic sensors can be widely used in energy source, security defense and other important fields, however their noise is complex, which affects the measurement accuracy and stability. Aiming at this problem, in this paper, an acoustic sensor system based on linear fiber optic Sagnac interferometer is demonstrated, and an improved wavelet threshold denoising algorithm is proposed. Furthermore, on this bases, combining with the signal characteristics, a synthesis filtering scheme is designed to improve the speech detection quality of the system. Taking the actually measured speech signal as an example, with this algorithm the Allan variance of the signal is reduced to 824×10-14, while the class spacing criterion is increased to 691, which effectively improve the quality of detected speech signal. The proposed algorithm can be widely used in acoustic sensing field, and has great significance for the accuracy of the later stage acoustic source localization for the optical fiber interferometer acoustic sensing system as well.