Here, we propose a Pt/HfO2/TaOx/TiN artificial synaptic device that is an excellent candidate for artificial synapses. First, XPS analysis is conducted to provide the dielectric (HfO2/TaOx/TiN) information deposited by DC sputtering and atomic layer deposition (ALD). The self-rectifying resistive switching characteristics are achieved by the asymmetric device stack, which is an advantage of the current suppression in the crossbar array structure. The results show that the programmed data are lost over time and that the decay rate, which is verified from the retention test, can be adjusted by controlling the compliance current (CC). Based on these properties, we emulate bio-synaptic characteristics, such as short-term plasticity (STP), long-term plasticity (LTP), and paired-pulse facilitation (PPF), in the self-rectifying I–V characteristics of the Pt/HfO2/TaOx/TiN bilayer memristor device. The PPF characteristics are mimicked by replacing the bio-stimulation with the interval time of paired pulse inputs. The typical potentiation and depression are also implemented by optimizing the set and reset pulse. Finally, we demonstrate the natural depression by varying the interval time between pulse inputs.