1. A synaptic transistor based on a metal nano-sheet, comprising: a gate electrode layer; a buffer layer disposed on the gate electrode layer; an insulating layer disposed on the buffer layer; a self-assembled floating gate layer disposed on the insulating layer; a channel layer disposed on the self-assembled floating gate layer; a source electrode layer disposed on one side of the channel layer; and a drain electrode layer disposed on the other side of the channel layer, the drain electrode layer being spaced apart from the source electrode layer, wherein the self-assembled floating gate layer comprises a metal oxide layer disposed on an external surface thereof and formed by naturally oxidization, and a metal layer disposed inside thereof.