The design of a compound microstructured optical fiber whose core is fabricated with the chalcogenide glass of As2Se3 and cladding made of tellurite glass is presented. The cladding is distributed with two rings of air holes. The dispersion and loss properties of the fiber is studied using a finite element method (FEM). With an adaptive split-step Fourier method-based solver for the generalized nonlinear schrodinger equation (GNLSE), the transmission of a 2.5 μm pump pulse with a width of 200 fs in a 15 cm fiber is numerically simulated. The properties of the infrared supercontinuum spectrum is also studied under different peak powers, pulse widths, and pump wavelengths.