With the intensification of the greenhouse effect, there is an increasing demand for monitoring the characteristic absorption bands of gases such as carbon dioxide in the mid- and far-infrared regions. The mid-infrared spectral region covers the typical molecular fingerprint region and includes the absorption band of greenhouse gases such as CO₂ around 15 μm. Blackbody radiation sources suffer from low brightness and poor coherence, whereas lasers exhibit high brightness but limited spectral bandwidth. Supercontinuum sources combine the advantages of both, offering broad spectral coverage, high brightness, and good coherence, and therefore demonstrate significant potential for infrared gas detection. However, commonly used nonlinear fibers, such as silica, fluoride, and tellurite fibers, still face certain limitations in terms of output performance. Chalcogenide glass possesses a broader mid- and far-infrared transmission range and a higher nonlinear coefficient, making it a promising candidate material for far-infrared supercontinuum generation. In this study, a novel telluride fiber was employed as the nonlinear medium to investigate far-infrared supercontinuum generation. Based on the split-step Fourier method, numerical simulations were performed to analyze the propagation dynamics of femtosecond pulses in the fiber and the corresponding evolution of the optical spectrum. The effects of fiber length, pump wavelength, and peak power on far-infrared supercontinuum spectral broadening were systematically investigated. Furthermore, far-infrared supercontinuum generation in the proposed fiber was numerically simulated using a 10.5 μm femtosecond pump pulse. The results show that the telluride fiber can generate broadband far-infrared supercontinuum output spanning 7–17 μm at a 40 dB intensity level under relatively low peak power conditions on the order of kilowatts. Therefore, this work provides a theoretical basis for the future design of far-infrared supercontinuum sources and is of great significance for the development of infrared spectroscopic applications.