Both synaptic emulators and brain-like calculation demand an energy-efficient and bio-realistic device where two-dimensional materials have been proven as a promising competitor. Lateral memristors based on transfer-free single-crystal MoS2 with single layer grown by chemical vapor deposition (CVD) were fabricated. Here the MoS2 memristor successfully emulates typical biological synaptic behaviors including excitatory/inhibitory post-synaptic current (EPSC/IPSC), spike timing-dependent plasticity (STDP), spike rate-dependent plasticity (SRDP) and long-term plasticity (LTP). Moreover, an interesting multi-state LTP and a low consumption of 1.8 pJ after LTP process are achieved which is attributed to the high resistance of transfer-free single-crystal monolayer MoS2, representing a low value among previous MoS2 devices. The migration of Sulfur vacancies lead the conductance modulation by changing the Schottky barrier instead of forming a filament. Our work demonstrates that MoS2 memristors can more flexibly satisfy the demands of complex artificial synaptic/neuron applications.