Hippocampal reverse replay is thought to contribute to learning, and particularly reinforcement learning, in animals. We present a computational model of learning in the hippocampus that builds on a previous model of the hippocampal-striatal network viewed as implementing a three-factor reinforcement learning rule. To augment this model with hippocampal reverse replay, a novel policy gradient learning rule is derived that associates place cell activity with responses in cells representing actions. This new model is evaluated using a simulated robot spatial navigation task inspired by the Morris water maze. Results show that reverse replay can accelerate learning from reinforcement, whilst improving stability and robustness over multiple trials. As implied by the neurobiological data, our study implies that reverse replay can make a significant positive contribution to reinforcement learning, although learning that is less efficient and less stable is possible in its absence. We conclude that reverse replay may enhance reinforcement learning in the mammalian hippocampal-striatal system rather than provide its core mechanism.