Membranes having perovskite structure are prominent ones, which show high proton conduction. Therefore, these membranes have been attracted attentions as not only for proton conduction solid oxide fuel cell but also for hydrogen separator. Among membranes of perovskite structure, BaZrO₃ is a likely candidate because of its stability under wide temperature condition and atmosphere. To design a high proton conductivity membrane, a number of studies has addressed about proton diffusion in membranes. However, it is difficult to elucidate the proton diffusion by experimental analysis because proton is small and can move faster than other ions in membranes. For this reason, molecular simulation is an effective way to address the proton diffusion. However, despite it has been pointed out that the quantum nature of proton appears in diffusion for years, the number of studies investigating the quantum effect of proton on its diffusion is very few. Hence, the quantum effect on proton diffusion remains unclear. In view of this, in this paper, the quantum effect of proton on its diffusion in BaZrO₃ membrane was analysed using molecular dynamics (MD) simulation based on the path integral (PI) notation. In this study, the quantum effect of proton on the two diffusion paths shown in Fig. 1 was addressed. First, the potential surface on each of the path was derived by using PIMD method. Where, because the quantum nature of proton depends on temperature, we derived the potential surface at five temperature conditions, which were 300 K, 400 K, 500 K, 800 K and 1000 K. Minimum energy positions were determined on each of the derived potential surface and minimum energy paths (MEP) between the minimum energy positions on each of the potential surface was derived by the nudged elastic band method. In this paper, the MEP was considered as the proton diffusion path and we evaluated the height of the potential barrier (energy difference between the maximum and the minimum energy position) along the MEP. Then, the diffusion rate of proton on each of the path was determined on the basis of the semi-classical transition state theory by using the potential barrier. Finally, the diffusion coefficient of proton in BaZrO₃ membrane was calculated using the determined diffusion rate. In this paper, 32 beads were allocated at the position of proton based on the PI notation. The calculation results were compared with that of classical case to elucidate the quantum effect of proton on its diffusion. As a result, it was found that the height of the potential barrier for path I increases with the decrease of temperature. On the other hand, the height of the potential barrier for path II decreases with the decrease of temperature due to the quantum effect of proton. Because of this difference in quantum effect on the paths, it was confirmed that the diffusion rate of proton is smaller than that of the classical case on path I, and the diffusion rate is large on path II. However, although influence of the quantum effect is different on each of the path, from the comparison of diffusion coefficient, it was clarified that the diffusion coefficient of the quantum case is rarely different from that of the classical case. These results indicate that although the quantum effect of proton affects the potential energy barrier for its diffusion path in BaZrO₃ membrane and its trend depends on the diffusion path, the quantum effect of proton does not appear in diffusion coefficient which is one of the bulk properties of BaZrO₃ membrane.