Chalcogenide fibers are currently being used widely in nonlinear optical signal processing, as they exhibit ultrahigh nonlinearity. Here, we propose a sensor based on stimulated Brillouin scattering for simultaneous temperature and strain measurement in a dual-core tapered As2Se3-polymethyl methacrylate fiber using a Brillouin optical time-domain analysis system. Different Brillouin frequency responses under temperature and strain variations and the separation of Brillouin frequency shifts (BFSs) in two principal polarization axes are demonstrated experimentally over a 50-cm-long tapered dual-core hybrid microfiber. The temperature coefficients are -3.8272MHz/∘C and -3.3302MHz/∘C, and the strain coefficients are -0.06143MHz/µε and -0.03463MHz/µε. Due to the different temperature and strain dependences of Brillouin frequency peaks in two polarizations, temperature and strain resolutions of 1°C and 33µε are realized, respectively. Numerical simulations are also reported to account for the BFS difference in two polarization axes.