The research paper presents a study of the effect of stress-induced martensite aging along the [001]A-deformation axis of the sample on both elastocaloric cooling capacity and superelasticity in Ni54Fe19Ga27 single crystals in compression. It has been experimentally shown that L10-martensite stabilization after the stress-induced martensite aging enhances the superelasticity parameters for the elastocaloric performance in the studied single crystals. In the stress-induced martensite aged Ni54Fe19Ga27 single crystals, the stress level of martensite formation σMs and stress hysteresis Δσ decrease by 130 MPa and by 16–17 MPa, respectively, compared with the as-grown crystals. Therefore, the stress-induced martensite aging increases the material efficiency for solid-state cooling systems: specific adiabatic temperature change per unit stress ΔTad/σMs increases by 4.4 times (ΔTad/σMs = 291.9 K/GPa (at Т = 348 K)) and coefficient of performance reaches COP = 24.5 in stress-induced martensite aged crystals as compared with the as-grown crystals (ΔTad/σMs = 62.4 K/GPa (at Т = 348 K), COP = 21.7). Smaller stress hysteresis corresponds to less energy dissipation in an operating cycle, which is also certainly useful for optimizing elastocaloric properties of a material. Moreover, both as-grown and stress-induced martensite aged crystals demonstrate high cyclic stability during loading/unloading cycles and weak temperature dependence of the elastocaloric cooling capacity ΔТad = 10.3–11.0 K in a wide operating temperature range up to 145–197 K. Thus, stress-induced martensite aged Ni54Fe19Ga27 single crystals oriented along the [001]А- direction are expected to be promising materials for elastocaloric application.