The AC electrical conductivity of LiBH4 was investigated below 2GPa between 1Hz and 1.6MHz. The high-temperature phase has an ionic conductivity of up to 0.01Scm(1), while the low-temperature phases have conductivities two orders of magnitude lower. All phases show an Arrhenius behaviour with activation energies E-a between 0.5 and 0.7eV, in good agreement with earlier data except for phase III, which is found to have the highest activation energy of the phases studied. The high-temperature phase has a minimum in E-a near 1GPa, close to the triple point, correlated with a sudden change in activation volume. These features may indicate an isostructural phase transition. The conductivities of the ambient temperature phases increase temporarily by an order of magnitude after transitions between these phases, probably due to new diffusion channels via structural defects. The phase diagram agrees well with earlier results