Adults commonly use spatial motion to talk about time. These metaphors are of at least three different types: moving-time, moving-ego, and sequence-as-relative-position-on-a-path. But when children grasp the meaning of spatial metaphors for time and what cognitive factors account for this understanding? In this study, we aim to answer these questions by studying young children’s comprehension of three different spatial metaphors for time. Our findings show that children begin to understand metaphors for time by age five and to explain the meaning of these different metaphors by age 6. Additionally, children’s comprehension varied by metaphor type, with moving-time and moving-ego metaphors being mastered earlier than sequence-as-relative-position-on-a-path metaphors. Moreover, we found children’s comprehension ability to be associated with their understanding of the time concept. Overall, these results suggest that comprehension of time metaphors is an early emerging linguistic ability that has strong ties to children’s cognitive understanding of the time concept.