In this work, a synaptic transistor based on the indium gallium zinc oxide (IGZO)–aluminum oxide (Al2O3) thin film structure, which uses ultraviolet (UV) light pulses as the pre-synaptic stimulus, has been demonstrated. The synaptic transistor exhibits the behavior of synaptic plasticity like the paired-pulse facilitation. In addition, it also shows the brain's memory behaviors including the transition from short-term memory to long-term memory and the Ebbinghaus forgetting curve. The synapse-like behavior and memory behaviors of the transistor are due to the trapping and detrapping processes of the holes, which are generated by the UV pulses, at the IGZO/Al2O3 interface and/or in the Al2O3 layer.