The effect of aging treatment on the superelasticity and martensitic transformation critical stress in columnar-grained Cu₇₁Al₁₈Mn₁₁ shape memory alloy (SMA) at the temperature ranging from 250°C to 400°C was investigated. The microstructure evolution during the aging treatment was characterized by optical microscopy, scanning electron microscopy, transmission electron microscopy, and X-ray diffraction. The results show that the plate-like bainite precipitates distribute homogeneously within austenitic grains and at grain boundaries. The volume fraction of bainite increases with the increase in aging temperature and aging time, which substantially improves the martensitic transformation critical stress of the alloy, whereas the bainite only slightly affects the superelasticity. This behavior is attributed to a coherent relationship between the bainite and the austenite, as well as to the bainite and the martensite exhibiting the same crystal structure. The variations of the martensitic transformation critical stress and the superelasticity of columnar-grained Cu₇₁Al₁₈Mn₁₁ SMA with aging temperature and aging time are described by the Austin–Rickett equation, where the activation energy of bainite precipitation is 77.2 kJ·mol⁻¹. Finally, a columnar-grained Cu₇₁Al₁₈Mn₁₁ SMA with both excellent superelasticity (5%–9%) and high martensitic transformation critical stress (443–677 MPa) is obtained through the application of the appropriate aging treatments.