We propose and experimentally demonstrate a high-resolution distributed measurement of the Brillouin gain spectrum in a polarization-maintaining fiber (PMF) using Brillouin dynamic grating. In our approach, acoustic waves which contain the information of the local Brillouin frequency are generated by a long pump pulse in one polarization along the PMF and are read out by a short probe pulse with an orthogonal polarization at a different optical frequency from the pump. In experiments, a distributed strain measurement with a 10 cm spatial resolution is demonstrated in a 105 m PMF.