The membranes having perovskite structure are prominent membranes, which shows high proton conduction. Therefore, these membrane have been attracted attentions as not only the membrane for the proton conduction solid oxide fuel cell but also for the hydrogen separator. Among the membranes of perovskite structure, BaZrO₃ is a likely candidate because of its stability under wide temperature condition and atmosphere. To design a membrane, which shows high proton conductivity, a number of studies has addressed the proton conduction in the membranes. However it is difficult to elucidate the proton conduction by experimental analysis because the proton is small and can move faster than other ions in the membrane. For this reason, analyses using molecular dynamics (MD) are effective ways to address the proton conduction. However, despite it has been pointed out that the quantum nature of the proton appears in the conduction for years, the number of studies investigating the quantum effect of the proton on its conduction is very few. Hence, the quantum effect on the proton conduction remains unclear. In view of this, in this paper, a quantum effect of the proton on its conduction in BaZrO₃ membrane was analysed using MD simulation based on the path integral (PI) notation. In this study, the quantum effect of the proton on the two conduction 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 the proton depends on the temperature, we derived the potential surface at four temperature conditions, which are 300K, 500K, 1000K and 2000K. Second, the minimum energy positions were determined on each of the derived potential surface by using the fast inertial relaxation engine algorithm. Finally, the 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 conduction path and we evaluated the height of the potential barrier (energy difference from the potential energy of the minimum energy position) along the MEP. In this paper, 32 beads were allocated at the position of the proton based on the PI notation. The breadth of the beads represents the quantum effect of the proton. The calculation results were compared with that of the classical case to elucidate the quantum effect of the proton on its conduction. As a result, it is confirmed that the potential energy on each of the path decreases and potential barrier varies because of the quantum effect of the proton. Moreover, it is cleared that the height of the potential barrier for the path I increases with a decrease of temperature. On the other hand, the height of the potential barrier for the path II decreases with a decrease of temperature due to the quantum effect of the proton. Besides, it is found that the minimum energy positions on the potential surface of path II is different from that of the previous works. We think that the cause of this distinction is the charges of the proton and the nearest oxygen ion. In this paper, the charges on the hydroxyl species are distributed so that the overall charge of the OH group is –1 with O and H assigned –1.4263 and 0.4263, respectively, which reproduces the dipole moment of the OH group. However, the previous papers do not consider the dipole moment of the OH group and the charges of the oxygen ion and proton were –2 and 1, respectively. From these results, it was clarified that the quantum effect of the proton affects the potential energy barrier for its conduction path in BaZrO₃ membrane about point a few eVs and the trend of the quantum effect on the potential energy barrier depends on the conduction path.