The synaptic properties of memristors have been widely studied. However, researchers are still committed to solving various challenges, including the study of highly reliable memristors with comprehensive synaptic functions and memristors that simulate highly complex neurological learning rules. In this work, we report a CeO 2 /Nb−SrTiO 3 heterojunction memristor whose conductance could be gradually tuned under both positive and negative pulse trains. Due to the gradual conductance switching behavior and the high switching ratio (10 5 ), the CeO 2 /Nb−SrTiO 3 heterojunction memristor could dutifully mimic biosynaptic functions, including excitatory/inhibitory postsynaptic current (EPSC/IPSC), paired-pulse facilitation and depression (PPF/PPD), spike amplitude-dependent plasticity (SADP), spike duration-dependent plasticity (SDDP), spike rate-dependent plasticity (SRDP), paired/triplet spiking-time-dependent plasticity (STDP), and Bienenstock−Cooper−Munro (BCM) rules. Moreover, a convolutional neural network based on the memristors is constructed to identify the electrocardiogram (ECG) data sets to realize the diagnosis of diseases with a recognition accuracy of 93%. Besides, the recognition accuracy of the handwriting digit reaches 96%. These studies broaden the research scope of high-level synaptic behavior and lay a foundation for the future full synaptic memristor networks.