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The structure, transition properties, and hydrostatic pressure (p) and magnetic field (B) dependence of transition temperatures and operation-temperature window (Δ T , defined as the temperature range of martensitic transition) were investigated in Ni 53 Mn 21 Ga 26 alloy. The results reveal that all the transition temperatures and Δ T increase almost linearly with increasing magnetic field and pressure. Particularly, a stronger dependence of peak temperature (T M) and Δ T on pressure, d T M /d p = 25.7 K/GPa and dΔ T /d p = 18.7–22.7 K/GPa, is observed in contrast with the smaller values of d T M /d B = 1.3 K/T and dΔ T /d B = 1.4–1.7 K/T found in Ni 53 Mn 21 Ga 26 alloy. Furthermore, the value of 25.7 K/GPa may be the largest shift in T M with pressure observed in polycrystalline Ni–Mn-Ga systems. Clearly, the sensitivities of T M and Δ T to pressure are much higher than those to magnetic field. These findings illustrate that applying hydrostatic pressure is beneficial to broaden Δ T in Ni 53 Mn 21 Ga 26 alloy. • Ni 53 Mn 21 Ga 26 alloy exhibits a magnetostructural transformation (MST). • Hydrostatic pressure effects on the phase transition properties and operation-temperature window (Δ T) have been studied. • A large shift in peak temperature with pressure of 25.7 K/GPa was observed. • A strong response of Δ T to pressure p , dΔ T /d p = 18.7–22.7 K/GPa, was reported. • Hydrostatic pressure can effectively broaden the operation-temperature window. [ABSTRACT FROM AUTHOR]