Owing to the conductance-adjustable performance, the emerging two-terminal memristors are promising candidates for artificial synapses and brain-spired neuromorphic computing. Although memristors based on molybdenum disulfide (MoS) have displayed outstanding performance, such as thermal stability and high energy efficiency, reports on memristors based on MoS as the functional layer to simulate synaptic behavior are limited. Herein, a homologous MoC/MoS-based memristor is prepared by partially sulfuring two-dimensional MoC crystal. The memristor shows good stability, excellent retention (~10 s) and endurance (>100 cycles), and a high ON/OFF ratio (>10). Moreover, for comprehensively mimicking biological synapses, the essential synaptic functions of the device are systematically analyzed, including paired-pulse facilitation (PPF), short-term plasticity (STP), long-term plasticity (LTP), long-term depression (LTD), and the transitions from STP to LTP. Notably, this artificial synapse could keep a high-level stable memory for a long time (60 s) after repeated stimulation. These results prove that our device is highly desirable for biological synapses, which show great potential for application in future high-density storage and neuromorphic computing systems.