Summary The hippocampus receives sequences of sensory inputs from the cortex during exploration and encodes the sequences with millisecond precision. We developed a predictive autoencoder model of the hippocampus including the trisynaptic and monosynaptic circuits from the entorhinal cortex (EC). CA3 was trained as a self-supervised recurrent neural network to predict its next input. We confirmed that CA3 is prediction ahead by analyzing the spike coupling between simultaneously recorded neurons in the dentate gyrus, CA3 and CA1 of the mouse hippocampus. In the model, CA1 neurons signal prediction errors by comparing the prediction from CA3 to the next input directly from the EC. The model exhibits the rapid appearance and the slow fading of CA1 place cells, and displays replay and phase precession from CA3. The model could be learnt in a biologically plausible way with the help of error-encoding neurons. Similarities between the circuits in the hippocampus and thalamocortical circuits suggest that such computation motif could also underlie self-supervised sequence learning in the cortex.