The use of electric vehicles has been increasing rapidly in recent years. Hence, determining the location of charging stations is a strategic decision. Managements may consider relocating charging stations as demand may change over time. In order to reflect the uncertainty in demand, it is appropriate to use fuzzy expressions. The demands of customers at present time can be calculated according to the criteria determined by using the fuzzy evaluations of decision makers. In this study, the single facility relocation problem for time-dependent demand is examined on finite time horizon. Rectilinear distance is considered. Demands of locations are calculated according to the criteria set by decision makers using cylindrical neutrosophic single-valued fuzzy expressions. This methodology is applied to the problem of minimum cost location of electric charging stations. The time-dependent demands of customers are determined with the help of cylindrical neutrosophic single-valued numbers. The minimum cost of relocating the charging station in a ten-year period is investigated. This application is intended to guide future facility relocation approaches.