The two-phase composite, LiF-MgF2, has been discovered to have high ionic conductivity within a wide composition range, e.g., 10(-2)-10(-1) S cm(-1) at 600-800 degreesC, which is several orders of magnitude higher than that of pure LiF or MgF2. In addition, the activation energy of the composite is much lower than that of the pure phases. The remarkable conductivity enhancement as well as the low activation energy is attributed to the composite effect, i.e., the conduction takes place mainly in the interfacial region between LiF and MgF2 grains. The agreements of conductivity derived from two different methods, impedance spectra and fuel cell characterisation, in combination of the ESR results, show a possibility that proton (plus hydride ion) conduction dominates the electrical conduction in the LiF-MgF2 system under the H-2/air fuel cell environments.