This work proposes a Penrose-based photonic quasi-crystal fiber (PQF) composed of Arsenic-free, non-toxic chalcogenide glass for Supercontinuum (SC) generation consisting of quasi-crystal lattice of air holes having eight-fold rotational symmetry. Following optimizing the structural parameters, the proposed PQF offers zero dispersion wavelength (ZDW) at around 3.8 μm, an effective mode area of 30 μm2, and a respective high nonlinearity of 824 W−1Km−1 at 2 μm wavelength. By injecting a secant hyperbolic optical pulse having a central wavelength of 4 μm with 20 kW peak power and pulse width of 50 fs, a broadband SC of 2–21 μm is generated, which mostly covers the transparency range of the proposed material as well as Mid-IR regime. To the best of our understanding, this particular type of PQF for broadband SC generation has been proposed for the first time, serving as the novelty factor. Apart from novelty, the wide-band SC assists the proposed PQF in becoming a better counterpart for applications like optical coherence tomography (OCT), frequency metrology, and other Mid-IR applications.