Artificial synaptic devices hold great potential in building neuromorphic computers. Due to the unique morphological features, two-dimensional organic semiconductors at the monolayer limit show interesting properties when acting as the active layers for organic field-effect transistors. Here, organic synaptic transistors are prepared with 1,4-bis ((5’-hexyl-2,2’-bithiophen-5-yl) ethyl) benzene (HTEB) monolayer molecular crystals. Functions similar to biological synapses, including excitatory postsynaptic current (EPSC), pair-pulse facilitation, and short/long-term memory, have been realized. The synaptic device achieves the minimum power consumption of 4.29 fJ at low drain voltage of −0.01 V. Moreover, the HTEB synaptic device exhibits excellent long-term memory with 10⁹ s EPSC estimated retention time. Brain-like functions such as dynamic learning-forgetting process and visual noise reduction are demonstrated by nine devices. The unique morphological features of the monolayer molecular semiconductors help to reveal the device working mechanism, and the synaptic behaviors of the devices can be attributed to oxygen induced energy level. This work shows the potential of artificial neuroelectronic devices based on organic monolayer molecular crystals.