Representing past, present and future locations is key for spatial navigation. Indeed, within each cycle of the theta oscillation, the population of hippocampal place cells appears to represent trajectories starting behind the current position of the animal and sweeping ahead of it. In particular, we reported recently that the position represented by CA1 place cells at a given theta phase corresponds to the location where animals were or will be located at a fixed time interval into the past or future assuming the animal ran at its typical, not the current, speed through that part of the environment. This coding scheme leads to longer theta trajectories, larger place fields and shallower phase precession in areas where animals typically run faster. Here we present a mechanistic computational model that accounts for these experimental observations. The model consists of a continuous attractor network with short-term synaptic facilitation and depression that internally generates theta sequences that advance at a fixed pace. Spatial locations are then mapped onto the active units via modified Hebbian plasticity. As a result, neighboring units become associated with spatial locations further apart where animals run faster, reproducing our earlier experimental results. The model also accounts for the higher density of place fields generally observed where animals slow down, such as around rewards. Furthermore, our modeling results reveal that an artifact of the decoding analysis might be partly responsible for the observation that theta trajectories start behind the animal’s current position. Overall, our results shed light on how the hippocampal code might arise from the interplay between behavior, sensory input and predefined network dynamics.