Molecular dynamics simulations are performed for a ZrF4-BaF2 glass system, which is expected to be a good ion-conducting material, in order to investigate the fundamental conduction dynamics of fluoride ions in the glass. The simulation results show that the ionic conduction is governed by the hopping motion of fluoride ions, with an average hopping distance of 2.5 AA, in the glass. This is clearly different from the diffusive motion observed in the melt. It is also found that the mobility is clearly different between bridging (Zr-F-Zr) and non-bridging (Zr-F-(Ba), (Ba)-F-(Ba)) fluoride ions in both glass and melt. The present result gives a satisfactory explanation of two distinct time scales observed in a previous NMR measurement (Y. Kawamoto and J. Fujiwara, 1990 Phys. Chem. Glasses 31 117). The first-passage-time approach is applied to the melt to determine the self-diffusion coefficients of the bridging and the non-bridging fluoride ions separately.