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High-entropy alloy (HEA) superconductors—a new class of functional materials—can be utilized stably under extreme conditions, such as in space environments, owing to their high mechanical hardness and excellent irradiation tolerance. However, the feasibility of practical applications of HEA superconductors has not yet been demonstrated because the critical current density (Jc) for HEA superconductors has not yet been adequately characterized. Here, we report the fabrication of high-quality superconducting (SC) thin films of Ta–Nb–Hf–Zr–Ti HEAs via a pulsed laser deposition. The thin films exhibit a large Jc of >1 MA cm−2 at 4.2 K and are therefore favorable for SC devices as well as large-scale applications. In addition, they show extremely robust superconductivity to irradiation-induced disorder controlled by the dose of Kr-ion irradiation. The superconductivity of the HEA films is more than 1000 times more resistant to displacement damage than that of other promising superconductors with technological applications, such as MgB2, Nb3Sn, Fe-based superconductors, and high-Tc cuprate superconductors. These results demonstrate that HEA superconductors have considerable potential for use under extreme conditions, such as in aerospace applications, nuclear fusion reactors, and high-field SC magnets.