A novel method to measure the refractive index change of a liquid around a fiber using stimulated Brillouin scattering generated dynamic grating is proposed. Two pump waves are used to generate a dynamic grating along a polarization maintaining (PM) fiber. The grating is then read by a probe wave. It is numerically shown that the frequency deviation of the pump and probe waves depends on the refractive index of liquid around the fiber. We consider three and four-hole suspended core (SC) fibers, in which one or two holes are filled with liquid, and investigate the change in the birefringence and the frequency deviation of the Brillouin dynamic grating due to the variation of the refractive index of liquid. The effects of fiber parameters on the sensitivity of frequency deviation as a function of liquid refractive index are discussed. We predict that a resolution of can be obtained using this method.