We demonstrate an optical time-domain distributed fiber sensor showing the highest spatial resolution ever reported based on Brillouin dynamic grating in a polarization-maintaining fiber. In our scheme, the acoustic gratings containing the information on the local Brillouin frequency are generated by a long pump pulse in one polarization, and read out by a short probe pulse in the orthogonal polarization at a clearly distinct optical frequency from the pump. In the experiment, distributed temperature measurements over a 20 m fiber are performed with 1.2 cm spatial resolution.