To detect weak underwater acoustic signal over large areas, an optical Distributed Acoustic Sensing(DAS) scheme based on space difference of Rayleigh backscattering was presented. In this scheme, Rayleigh backscattered light with phase changes induced by the acoustic signal along a single-mode sensing fiber was split and fed into an imbalanced Michelson interferometer. Adjusting the path difference of the imbalanced Michelson interferometer, the Rayleigh backscattered light interference of different lengths of adjacent space segments along the sensing fiber was realized. Subsequently, the phase information including the acoustic signal was demodulated by the 3×3 coupler demodulation technology. An underwater acoustic wave measuring system based on DAS was implemented, which can not only locate the two acoustic positions accurately in real time, but also restore the amplitude, frequency and phase of sound waves. In addition, the acoustic phase sensitivity is -148.8 dB(re rad/μPa) at 1 kHz, and the frequency response flatness at frequencies ranging from 100 Hz to 1 500 Hz is within 1.2 dB. The experimental results confirm that the novel Φ-OTDR technology can enable quantitative measurements of multiple acoustic information in real time.