The crystal structure of the Li2UBr6 ionic conductor has been studied as a function of the temperature by powder neutron diffraction. The room and high temperature structures have been determined. At 300 K the compound crystallises in a trigonal unit cell (space group P-31m) with lattice constants : a = b = 6.8893(4), c = 12.6462(9) Angstrom. Above the phase transitions occurring at 505 K the space group is found to be monoclinic C2/m. The mechanism of ionic conductivity is discussed.