The current of the residential series arc fault is affected by the load type, and the fault feature change is not obvious and contains noise. Therefore, the extraction of fault features will affect the arc fault detection results. To solve this problem, an improved salp swarm optimization algorithm combined with variational mode decomposition is proposed to extract the characteristics of current signal, improve the decomposition effect of current signal, and construct a dataset that can fully reflect the characteristics of arc fault. The ReliefF algorithm is designed to combine minimum redundancy maximum relevance to reduce the feature dimension and eliminate redundancy. Finally, the random forest model is used to diagnose the fault, which can quickly detect the fault and does not cause over-fitting. Experiments based on the self-built sample set prove that the arc fault can be quickly detected under different acquisition frequencies and noise environments, and the detection rate is more than 95%.