The grid cells in the entorhinal cortex play fundamental roles in spatial navigation. However, it has been unclear whether they contribute to predicting an animal’s future location or determining its future trajectory. In this study, we performed large-scale extracellular recordings from the medial entorhinal cortex together with hippocampal CA1 of rats moving toward a destination in the square arena. We found a subset of grid cells in the medial entorhinal cortex that represent grid fields when rate maps are estimated based on future animal locations, but these cells did not show grid field based on current animal locations. These predictive grid cells represent prospective spatial information by shifting their grid fields anteriorly direction relative to the animal's direction of travel. Interestingly, predictive grid cells discharged at the trough phases of the CA1 theta oscillation. We further analyzed the differences from traditional grid cells in layers 2 and 3, and found that each grid cell discharged at the different theta phases, indicating that these grid cells organized sequences of the trajectories from the current to future positions across each theta cycle. Furthermore, we confirmed the functional connectivity between predictive grid cells and hippocampal CA1 place cells, suggesting that predictive grid cells are likely to transmit future information to the hippocampus. Our results suggest that the predictive grid cells make a significant contribution to the spatial navigation in terms of predicting future trajectories.