Anticipating the future is a key motif of the brain, possibly supported by mental simulation of upcoming events. Rodent single-cell recordings suggest the ability of spatially tuned cells to represent subsequent locations. Grid-like representations have been observed in the human entorhinal cortex during virtual and imagined navigation. However, hitherto it remains unknown if grid-like representations contribute to mental simulation in the absence of imagined movement. Participants imagined directions between building locations in a large-scale virtual-reality city while undergoing fMRI without re-exposure to the environment. Using multi-voxel pattern analysis, we provide evidence for representations of absolute imagined direction at a resolution of 30° in the parahippocampal gyrus, consistent with the head-direction system. Furthermore, we capitalize on the six-fold rotational symmetry of grid-cell firing to demonstrate a 60° periodic pattern-similarity structure in the entorhinal cortex. Our findings imply a role of the entorhinal grid-system in mental simulation and future thinking beyond spatial navigation.