The posterior cerebellum is responsible for the understanding and learning of sequences of actions by others, which are a prerequisite for social understanding. This study investigates this cerebellar function while navigating towards a goal in a social context. Participants undertook a novel social navigation task requiring them to memorize and subsequently reproduce a protagonist's trajectory through a grid towards a desirable goal. As a non-social control condition, a ball underwent the same trajectory by passively rolling through the grid toward the same endpoint. To establish that memorizing and reproducing a trajectory is a critical cerebellar function, two non-sequencing control conditions were created, which involved the observation only of the trajectory by the protagonist or ball. Our results showed that the posterior cerebellar Crus II was involved in memorizing both social and non-social trajectories, along with the parahippocampal gyrus and other cortical areas involved in social cognition. As hypothesized, cerebellar Crus I was more active when memorizing social as opposed to non-social trajectories. Moreover, cerebellar Crus I and II, and lobule VI, were activated when reproducing both social and non-social trajectories. These findings highlight the involvement of the posterior cerebellar Crus in supporting human goal-directed social navigation.