Human agents build models of their environment, which enable them to anticipate and plan upcoming events. However, little is known about the properties of such predictive models. Recently, it has been proposed that hippocampal representations take the form of a predictive map-like structure, the so-called successor representation. Here we used human fMRI to probe whether activity in the early visual cortex (V1) and hippocampus adhere to the postulated properties of the successor representation after visual sequence learning. Participants were exposed to an arbitrary spatiotemporal sequence consisting of four items (A-B-C-D). We found that after repeated exposure to the sequence, merely presenting single sequence items (e.g., - B - -) resulted in V1 activation at the successor locations of the full sequence (e.g., C-D), but not at the predecessor locations (e.g., A). This highlights that visual representations are skewed toward future states, in line with the successor representation. Similar results were also found in the hippocampus. Moreover, the hippocampus developed a tuning profile that showed sensitivity to the temporal distance in sequence-space, with fading representations for sequence events in the more distant past and future. V1, in contrast, showed a tuning profile that was only sensitive to spatial distance in stimulus-space. Together, these results provide empirical evidence for the proposition that both visual and hippocampal cortex represent a predictive map of the visual world akin to the successor representation.