Shape-memory alloys suitable for low-temperature environments are crucially lacking despite their potential applications for aerospace engineering, superconducting technologies, and liquefied-gas-storage technologies. Even for benchmark shape-memory alloys such as Ti–Ni and Ni-based Heusler alloys, superelasticity becomes appreciably difficult to achieve upon cooling because of a drastic increase in stress hysteresis. Here, we report a superelastic strain of more than 7% for a Cu–Al–Mn shape-memory alloy down to 4.2 K with stress hysteresis as small as that at ambient temperature. Furthermore, the transformation entropy change remains as large as that at ambient temperature down to ~50 K. Consequently, an excellent elastocaloric cooling property is simultaneously obtained even at cryogenic temperatures, at which existing shape-memory alloys lose this property because of decreased entropy change and increased stress hysteresis. The developed cryogenic superelastic alloy shows excellent potential as a new class of material combining superelastic properties with sufficiently small dissipated energy and persistent elastocaloric cooling ability even in cryogenic environments.