We experimentally demonstrate that the reflection spectrum of a Brillouin dynamic grating in a polarization-maintaining fiber can be much narrower than the intrinsic linewidth of the stimulated Brillouin scattering, matching well with the theory of a fiber Bragg grating in terms of the linewidth and the reflectivity. A 3 dB bandwidth as narrow as 10.5 MHz is observed with the Brillouin dynamic grating generated in a 9 m uniform fiber.