The Brillouin gain properties in a double-clad As2Se3 photonic crystal fiber (PCF) are simulated based on the finite-element method (FEM). The results indicate that the Brillouin gain spectrum (BGS) of our proposed chalcogenide PCF exhibits a multipeaked behavior and has a high Brillouin gain coefficient. We also find that a larger size of inner cladding air holes will lead to a more pronounced second peak in the BGS. On the other hand, the size of the outer cladding has nearly no effect on the BGS behavior. Through these results, one can tailor the Stimulated Brillouin scattering effect in PCFs for a wide range of applications.