The principle and architecture of an interferometric fiber acoustic sensor based on sawtooth wave optical frequency modulated continuous wave are introduced. Firstly, the beat signal and its spectrum are theoretically analyzed, and a digital demodulation method is described. Secondly a corresponding experimental system is built to analyze the spectrum. Digital demodulation with 10 m and 20 m arm difference of interferometers is finished under 10 kHz sawtooth wave optical frequency modulated. The experimental results show that this sensor is a heterodyne interferometer but without frequency shifters and a frequency division multiplexing system can be easily got by changing the arm difference of interferometers. It can be used in all optical, long distance faint acoustic vibration detection under complicated condition.