Energy-efficient and environment-friendly elastocaloric refrigeration, which is a promising replacement of the conventional vapor-compression refrigeration, requires extraordinary elastocaloric properties. Hitherto the largest elastocaloric effect is obtained in small-size films and wires of the prototype NiTi system. Here, we report a colossal elastocaloric effect, well exceeding that of NiTi alloys, in a class of bulk polycrystalline NiMn-based materials designed with the criterion of simultaneously having large volume change across phase transition and good mechanical properties. The reversible adiabatic temperature change reaches a strikingly high value of 31.5 K and the isothermal entropy change is as large as 45 J kg^{-1} K^{-1}. The achievement of such a colossal elastocaloric effect in bulk polycrystalline materials should push a significant step forward towards large-scale elastocaloric refrigeration applications. Moreover, our design strategy may inspire the discovery of giant caloric effects in a broad range of ferroelastic materials.