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Recent experimental observations have shown that the reactivation of hippocampal place cells (PC) during sleep or immobility depicts trajectories that can go around barriers and can flexibly adapt to a changing maze layout. Such layout-conforming replay sheds a light on how the activity of place cells supports the learning of flexible navigation of an animal in a dynamically changing maze. However, existing computational models of replay fall short of generating layout-conforming replay, restricting their usage to simple environments, like linear tracks or open fields. In this paper, we propose a computational model that generates layout-conforming replay and explains how such replay drives the learning of flexible navigation in a maze. First, we propose a Hebbian-like rule to learn the inter-PC synaptic strength during exploring a maze. Then we use a continuous attractor network (CAN) with feedback inhibition to model the interaction among place cells and hippocampal interneurons. The activity bump of place cells drifts along a path in the maze, which models layout-conforming replay. During replay in rest, the synaptic strengths from place cells to striatal medium spiny neurons (MSN) are learned by a novel dopamine-modulated three-factor rule to store place-reward associations. During goal-directed navigation, the CAN periodically generates replay trajectories from the animal's location for path planning, and the trajectory leading to a maximal MSN activity is followed by the animal. We have implemented our model into a high-fidelity virtual rat in the MuJoCo physics simulator. Extensive experiments have demonstrated that its superior flexibility during navigation in a maze is due to a continuous re-learning of inter-PC and PC-MSN synaptic strength.