The highly parallel artificial neural systems based on transistor-like devices have recently attracted widespread attention due to their high-efficiency computing potential and the ability to mimic biological neurobehavior. For the past decades, plenty of breakthroughs related to synaptic transistors have been investigated and reported. In this work, a kind of photoelectronic transistor that successfully mimics the behaviors of biological synapses has been proposed and systematically analyzed. For the individual device, MXenes and the self-assembled titanium dioxide on the nanosheet surface serve as floating gate and tunneling layers, respectively. As the unit electronics of the neural network, the typical synaptic behaviors and the reliable memory stability of the synaptic transistors have been demonstrated through the voltage test. Furthermore, for the first time, the UV-responsive synaptic properties of the MXenes floating gated transistor and its applications, including conditional reflex and supervised learning, have been measured and realized. These photoelectric synapse characteristics illustrate the great potential of the device in bio-imitation vision applications. Finally, through the simulation based on an artificial neural network algorithm, the device successfully realizes the recognition application of handwritten digital images. Thus, this article provides a highly feasible solution for applying artificial synaptic devices to hardware neuromorphic networks.