Novel computing technologies that imitate the principles of biological neural systems may serve low power consumption with significant cognitive and learning advantages. The development of memristors with non-volatile memory characteristics has opened up new applications in neuromorphic circuits and adaptive systems. However, conventional metal oxide memristor devices are generally based on oxygen vacancy or metal-ion conductive filament mechanisms that make it hard to realize the function of neuromorphic computing. Herein, we demonstrate that CrSBr nanosheet-based memristor exhibits high durability, low power consumption, and the capacity to achieve multiple reproducible resistance states, displaying resistive switching performance. Furthermore, we successfully simulated various synaptic behaviors, such as short-term/long-term plasticity, paired-pulse facilitation (PPF), and spike-timing-dependent plasticity (STDP), revealing the capability of CrSBr memristors to flexibly meet the demands of complex neuromorphic computing applications. Our work makes CrSBr a promising candidate which is considered to be the behavior of an ideal synaptic biomimetic device in future computing systems.