A novel inorganic-organic hybrid compound, allylammonium hexabromobismuthate(III), (C3H5NH3)3BiBr6 (ABB), was synthesised and its structure determined by means of single-crystal X-ray diffraction studies at four temperatures (280, 230, 170 and 100 K). At 100 K, the compound crystallises in the monoclinic space group, C2/c. Its crystal structure consists of discrete BiBr63– anions and three inequivalent allylammonium (C3H5NH3)+ cations. Four solid-solid structural phase transitions for ABB were detectable by means of DSC and dilatometric techniques: continuous (I↔II) at 272/272 K (upon heating/cooling), discontinuous (II↔III) at 218/215, discontinuous (III↔IV) at 205/204 K and discontinuous (IV↔V) at 146/144 K. The ferroelastic domain structure was observed over one intermediate phase (III) below 215 K. The electric properties of ABB have been measured over a wide temperature range (105–310 K). Low frequency relaxation processes with dielectric increments Δϵ1 ≈ 0.9 and Δϵ2 ≈ 0.05 were observed within phases II and V, respectively. Temperature-dependent vibrational properties of ABB in the frequency region 3500–500 cm–1 and the molecular motions of its allylammonium cations were studied by means of proton magnetic resonance. The mechanisms of the phase transitions in the title compound are discussed.