A J0-J1 method for measurement of dynamic phase changes in an interferometric optical fiber sensor is described. This method has the advantages of no electric elements in the sensing head and the simplicity of signal processing. The detection principle of this method is introduced in details. The demodulation error is analyzed and simulated theoretically. The measurable amplitude of the dynamic phase change and the permitted varying range of the work-point restrict each other. A system of data acquisition and processing is programmed, and an interferometric fiber-optic hydrophone is tested. The average acoustic pressure sensitivity is -162 dB (0 dB=1 rad/μPa) over the frequency range of 20 Hz to 1300 Hz, the fluctuation is smaller than ±1.0 dB, and the change at 500 Hz is smaller than ±0.5 dB, which accords well with the results obtained with the method of phase generated carrier (PGC) modulation and demodulation. The experimental results prove that this J0-J1 method is feasible.