We investigated proton conduction across and along energetically favorable BaO- and ZrO2-terminated (001) BaZrO3 surfaces by using density functional theory. The proton concentration at the surfaces was evaluated from the space charge model using the proton segregation energy. The proton was segregated at the ZrO2-terminated surface more than the BaO-terminated surface. The proton mobility across and along the surfaces was evaluated from the proton migration barrier. The proton mobility along the ZrO2-terminated surface was highest among the four pathways. Therefore, from the product of the concentration and mobility, the proton can conduct easily along the ZrO2-terminated (001) surface. The proton conduction along the ZrO2-terminated (001) surface can help find a potentially easy path, such as surface grain boundaries and triple phase boundaries.