In this work, we introduce a new family of barocaloric hybrid organic-inorganic compounds with colossal barocaloric effects. The here reported hybrid materials, [(CH3)3(CH2Cl)N]FeCl4 and [(CH3)3S]FeCl4, exhibit a molecular structure composed by discrete inorganic anions and organic cations with weak elestrostatic interactions. Our calorimetric studies reveal colossal barocaloric effects of similar magnitude than organic plastic crystals (ΔS > 100 J K-1 kg-1) near room temperature and under smaller pressures (p ≤ 1000 bar), which leads to higher barocaloric strengths. Furthermore, these materials exhibit densities similar to barocaloric hybrid perovskites enhancing the volumetric barocaloric effects (ΔS ~ 200 J K-1 l-1), which could provide more compact cooling devices. Therefore, the colossal values of the mass and volumetric barocaloric effects and large barocaloric strength, in addition to the low working pressure and near-room-temperature operation, offer a new family of compounds to further explore in the search for improved barocaloric materials.