Neural networks are computing models based on human brains. We propose a neural network using a field-programmable gate array (FPGA) for neurons and amorphous In-Ga-Zn-O (a-IGZO) thin films for synapses. It is found that electric current in the a-IGZO thin film gradually decreases along the time. On the other hand, the degradation does not occur when light is irradiated. These phenomena can be utilized for the synapses in the neural network. It is confirmed that after the learning, the neural network replies the correct answer of AND logic. These results indicate that the neural networks using a-IGZO thin films have a great potential to realize future neural networks.