Caloric effects are currently under intense study due to the prospect of environment-friendly cooling applications. Most of the research is centred on large magnetocaloric effects and large electrocaloric effects, but the former require large magnetic fields that are challenging to generate economically and the latter require large electric fields that can only be applied without breakdown in thin samples. Here we use small changes in hydrostatic pressure to drive giant inverse barocaloric effects near the ferrielectric phase transition in ammonium sulphate. We find barocaloric effects and strengths that exceed those previously observed near magnetostructural phase transitions in magnetic materials. Our findings should therefore inspire the discovery of giant barocaloric effects in a wide range of unexplored ferroelectric materials, ultimately leading to barocaloric cooling devices.