Highly nonlinear chalcogenide fibers are widely used in the applications of Brillouin fiber sensing and fiber lasing. A stimulated Brillouin scattering (SBS) dual-parameter sensing method based on a highly birefringent chalcogenide polymer composite fiber (As₂Se₃-PMMA) was introduced, a highly nonlinear elliptical-core As₂Se₃-PMMA tapered fiber was designed and fabricated, and the SBS characteristics of the fiber were measured using a Brillouin optical time-domain analysis (BOTDA) system. Due to different Brillouin frequency shifts of temperature and strain in the fast and slow axes of the elliptical-core As₂Se₃-PMMA tapered fiber, the dual-parameter measurement of temperature and strain of the sensor was achieved. The temperature sensitivities in the fast and slow axes of the elliptical-core chalcogenide tapered fiber are ?2.772 MHz/°C and ?2.605 MHz/°C, respectively, and strain sensitivities are ?21.9 kHz/με and ?16.3 kHz/με, respectively. By establishing a matrix based on the different temperatures and strain responses of the fast and slow axes, the temperature and strain resolution of the chalcogenide optical fiber sensor are 0.9 °C and 28 με, respectively.