Real-time fault detection is important for operation of smart grid. It has become a trend of future development to design an anomaly detection system based on deep learning by using the powerful computing power of the cloud. However, delay of Internet transmission is large, which may make the delay time of detection and transmission go beyond the limits. However, the edge-based scheme may not be able to undertake all data detection tasks due to limited computing resources of edge devices. Therefore, we propose a cloud-edge collaborative smart grid fault detection system, next to which edge devices are placed, and equipped with a lightweight neural network with different precision for fault detection. In addition, a sub-optimal and real-time communication and computing resource allocation method is proposed based on deep reinforcement learning. This method greatly speeds up solution time, which can meet the requirements of data transmission delay, maximize the system throughput, and improve communication efficiency. Simulation results show the scheme is superior in transmission delay and improves real-time performance of the smart grid detection system.