In this study, we propose and demonstrate a distributed sensor based on weak-reflection fiber Bragg grating (WFBG) to detect the acoustic wave direction. Further, we utilize a distributed sensing fiber between two adjacent WFBGs to detect the sound vibration signals. The phase difference of the demodulation signals of two sensing fibers corresponds to the difference between the reaching times of the acoustic wave, and the sound direction can be calculated based on the time difference. A 50-m sensing fiber coil is placed in vibration liquid column, and the average sound pressure sensitivity is estimated to be -155.10 dB (re rad/μPa). Two 50-m sensing fibers are distributed on the wooden floor. Sinusoidal sound signals are received, and the root mean square error of the detection direction is 1.35°. The principle deduction and experimental results prove that the acoustic wave direction can be detected using the proposed sensor. It is expected to be carried on an unmanned underwater vehicle to detect the underwater vocal target because of the smaller size of the proposed structure when compared with that of the traditional structure of the fiber twined on substrate.