The magnetocaloric effect (MCE) in paramagnetic materials has been widely used for attaining very low temperatures by applying a magnetic field isothermally and removing it adiabatically. The effect can also be exploited for room-temperature refrigeration by using giant MCE materials(1-3). Here we report on an inverse situation in Ni-Mn-Sn alloys, whereby applying a magnetic field adiabatically, rather than removing it, causes the sample to cool. This has been known to occur in some intermetallic compounds, for which a moderate entropy increase can be induced when a field is applied, thus giving rise to an inverse magnetocaloric effect(4,5). However, the entropy change found for some ferromagnetic Ni-Mn-Sn alloys is just as large as that reported for giant MCE materials, but with opposite sign. The giant inverse MCE has its origin in a martensitic phase transformation that modifies the magnetic exchange interactions through the change in the lattice parameters.