Low-voltage arc fault detection can effectively prevent fires, electric shocks, and other accidents, reducing potential risks to human life and property. The research on arc fault circuit interrupters (AFCIs) is of great significance for both safety in production scenarios and daily living disaster prevention. Considering the diverse characteristics of loads between the normal operational state and the arc fault condition, a parallel neural network structure is proposed for arc fault recognition, which is based on a convolutional neural network (CNN) and a Transformer. The network uses convolutional layers and Transformer encoders to process the low-frequency current and high-frequency components, respectively. Then, it uses Softmax classification to perform supervised learning on the concatenated features. The method combines the advantages of both networks and effectively reduces the required depth and computational complexity. The experimental results show that the accuracy of this method can reach 99.74%, and with the threshold-moving method, the erroneous judgment rate can be lower. These results indicate that the parallel neural network can definitely detect arc faults and also improve recognition efficiency due to its lean structure.