We have conducted a study on a very-low-frequency acoustic-velocity sensor which is based on a cantilever of distributed-feedback (DFB) fiber laser immersed in castor oil. A mathematical model of the frequency dependent response of the proposed sensor to the acoustic pressure signal influenced by the fluid viscosity is established. We have fabricated the proposed sensor and conducted experimental measurements in the standing wave tube. The results show that the sensor has an average phase sensitivity of −179.5 dB (0 dB = 1 rad/μPa) with ±1.45 dB fluctuation over the frequency range of 20–38 Hz. It has good cosine directivity with a directivity index of 32.5 dB and axial maximum asymmetry of 0.4 dB. The sensor presents promising applications for detecting very-low-frequency underwater acoustic signals.