Nowadays, memristors are extremely similar to biological synapses and can achieve many basic functions of biological synapses, making them become a new generation of research hotspots for brain-like neurocomputing. In this work, we prepare a memristor based on two-dimensional α-In 2 Se 3 nanosheets, which exhibits excellent electrical properties, faster switching speeds, and continuous tunability of device conduction. Meanwhile, most basic bio-synapse functions can be implemented faithfully, such as short-term memory (STM), long-term memory (LTM), four different types of spike-timing-dependent plasticity (STDP), and paired-pulse facilitation (PPF). More importantly, we systematically study three effective methods to achieve LTM, in which the reinforcement learning can be faithfully simulated according to the Ebbinghaus forgetting curve. Therefore, we believe this work will promote the development of learning functions for brain-like computing and artificial intelligence.