The entorhinal cortex represents allocentric spatial geometry and egocentric speed and heading information required for spatial navigation. However, it remains unclear whether it contributes to the prediction of an animal’s future location. We discovered grid cells in the medial entorhinal cortex (MEC) that have grid fields representing future locations during goal-directed behavior. These predictive grid cells represented prospective spatial information by shifting their grid fields against the direction of travel. Predictive grid cells discharged at the trough phases of the hippocampal CA1 theta oscillation and, together with other types of grid cells, organized sequences of the trajectory from the current to future positions across each theta cycle. Our results suggest that the MEC provides a predictive map that supports forward planning in spatial navigation.