With the advent of brain-inspired computing for complex data processing, emerging nonvolatile memories have been widely studied to develop neuromorphic devices for pattern recognition and deep learning. However, the devices still suffer from limitations such as nonlinearity and large write noise because they adopt a stochastic switching approach. Here, we suggest a biomimetic three-terminal electrochemical artificial synapse that is operated by a conductance change in response to intercalation of sodium (Na+) ions into a layered SnS2-reduced graphene oxide (RGO) composite channel. SnS2-RGO can reversibly uptake and release Na+ ions, so the conductance of the channel in artificial synapse can be controlled effectively and thereby it can emulate essential synaptic functions including short-term plasticity, spatiotemporal signal processing, and transition from short-term to long-term plasticity. The artificial synapse also shows linear and symmetric potentiation/depression with low cycle-to-cycle variation; these responses could improve the write linearity and reduce the write noise of devices. This study demonstrates the feasibility of next-generation neuromorphic memory using ion-based electrochemical devices that can mimic biological synapses with the migration of Na+ ions.