A composite glass, CuI-Cu2MoO4, has an ionic conductivity at room temperature, corresponding to ionic liquid conductivity. Pulsed neutron scattering and XAFS measurements show that the main framework of the sample is constructed from [MoO4]-tetrahedra and [MoO6]-octahedra. Cu+ ions in the glass are bound to 2 O atoms or 4 I atoms. he atomic motion below 20 meV in the sample measured at room temperature is close to that of the α-CuI crystalline state near its melting point. In addition to the Boson peak, above 200 K, quasielastic neutron scattering due to the local diffusion of Cu+ ions is found at energies 5 meV. The long-range translational diffusion of the Cu+ ions in the sample is directly demonstrated by high resolution quasielastic neutron scattering results. The broadening is less than 100 μeV. The hierarchic static and dynamic structure of the sample is shown to control the properties of the super-ionic conducting glass, CuI-Cu2MoO4.