We report giant reversible barocaloric effects in [(CH3)4N]Mn[N3]3 hybrid organic–inorganic perovskite, near its first-order cubic-monoclinic structural phase transition at T0 ∼ 305 K. When driving the transition thermally at atmospheric pressure, the transition displays a large change in entropy of ∼80 J K−1 kg−1 and a small thermal hysteresis of ∼7 K, as well as a large change in volume of ∼1.5%. When driving the transition with pressure near room temperature, the transition displays large changes in entropy of ∼70 J K−1 kg−1, which represent a giant barocaloric response. Hybrid perovskites with similar barocaloric response and lower operating temperatures may find applications in environmentally friendly cooling.