Compared with conventional computation relying on the von Neumann architecture, brain-inspired computing has shown superior strength in various cognitive tasks. It has been generally accepted that information in the brain is represented and formed by vastly interconnected synapses. So the physical implementation of electronic synaptic devices is crucial to the development of brain-based computing systems. Among a large number of electronic synaptic devices, the memristors have attracted significant attention due to its simple structure and similarities to biological synapses. In this work, we first use two-dimensional material MXene as a resistive material and fabricate an electronic synapse based on a Cu/MXene/SiO₂/W memristor. By using the unique properties of MXene, the conductance of the memristor can be modulated by the accumulation or reflux of Cu²⁺ at the physical switching layer, which can vividly simulate the mechanism of bio-synapses. Experimental results show that the Cu/MXene/SiO₂/W memristor not only achieves stable bipolar analog resistance switching but also shows excellent long-term and short-term synaptic behaviors, including paired-pulse facilitation (PPF) and long-term potential/depression. By adjusting the pulse interval, the PPF index will change accordingly. In a biological system, the short-term plasticity is considered to be the key point for performing computational functions while the long-term plasticity is believed to underpin learning and memory functions. This work indicates that Cu/MXene/SiO₂/W memristor with both long-term and short-term plasticity will have great application prospects for brain-inspired intelligence in the future.