The advent of memristors and the continuing research and development in the field of brain-inspired computing could allow realization of a veritable “thinking machine”. In this study, ZnO-based memristors were fabricated using a radio frequency magnetron sputtering method. The ZnO oxide layer was prepared by incorporating silver nanocrystals (NCs). Several synaptic functions, i.e. nonlinear transmission characteristics, short-term potentiation, long-term potentiation/depression, and pair-pulse facilitation, were imitated in the memristor successfully. Furthermore, the transition from synaptic behaviors to bipolar resistive switching behaviors of the device was also observed under repeated stimulus. It is speculated that the switching mechanism is due to the formation and rupture of the conductive Ag filaments and the corresponding electrochemical metallization. The experimental results demonstrate that the Ag/Ag:ZnO/Pt memristor with resistive switching and several synaptic behaviors has a potential application in neuromorphic computing and data storage systems.