The power supply quality and power supply safety of a low-voltage residential power distribution system is seriously affected by the occurrence of series arc faults. It is difficult to detect and extinguish them due to the characteristics of small current, high stochasticity, and strong concealment. In order to improve the overall safety of residential distribution systems, a novel method based on discrete wavelet transform (DWT) and deep neural network (DNN) is proposed to detect series arc faults in this paper. An experimental bed is built to obtain current signals under two states, normal and arcing. The collected signals are discomposed in different scales applying the DWT. The wavelet coefficient sequences are used for forming training set and test set. The deep neural network trained by training set under 4 different loads adaptively learn the feature of arc faults. The accuracy of arc faults recognition is sent through feeding test set into the model, about 97.75%. The experimental result shows that this method has good accuracy and generality under different types of loading.