Synaptic nano-devices have powerful capabilities in logic, memory and learning, making them essential components for constructing brain-like neuromorphic computing systems. Here, we have successfully developed and demonstrated a synaptic nano-device based on Ga₂O₃ nanowires with low energy consumption. Under 255 nm light stimulation, the biomimetic synaptic nano-device can stimulate various functionalities of biological synapses, including pulse facilitation, peak time-dependent plasticity and memory learning ability. It is found that the artificial synaptic device based on Ga₂O₃ nanowires can achieve an excellent "learning-forgetting-relearning" functionality. The transition from short-term memory to long-term memory and retention of the memory level after the stepwise learning can attribute to the great relearning functionality of Ga₂O₃ nanowires. Furthermore, the energy consumption of the synaptic nano-device can be lower than 2.39 × 10^‒11 J for a synaptic event. Moreover, our device demonstrates exceptional stability in long-term stimulation and storage. In the application of neural morphological computation, the accuracy of digit recognition exceeds 90% after 12 training sessions, indicating the strong learning capability of the cognitive system composed of this synaptic nano-device. Therefore, our work paves an effective way for advancing hardware-based neural morphological computation and artificial intelligence systems requiring low power consumption.