A temperature-compensated distributed hydrostatic pressure sensor based on Brillouin dynamic gratings (BDGs) is proposed and demonstrated experimentally for the first time, to the best of our knowledge. The principle is to measure the hydrostatic pressure induced birefringence changes through exciting and probing the BDGs in a thin-diameter pure silica polarization-maintaining photonic crystal fiber. The temperature cross-talk to the hydrostatic pressure sensing can be compensated through measuring the temperature-induced Brillouin frequency shift (BFS) changes using Brillouin optical time-domain analysis. A distributed measurement of hydrostatic pressure is demonstrated experimentally using a 4-m sensing fiber, which has a high sensitivity, with a maximum measurement error less than 0.03 MPa at a 20-cm spatial resolution.