The load and operating status of low-voltage distribution network have significant dynamic variation features, including load fluctuations, equipment aging, and faults, which increase the difficulty of safety assessment. To effectively address this challenge, a low-voltage distribution network security analysis method based on three-layer BP(back propagation) neural network algorithm is proposed. This method uses power quality, current voltage harmonic distortion, and feeder capacity as safety evaluation indicators. The normalized real-time operating status data is input into a three-layer BP neural network, and the weight values of each level of the network are corrected based on the safety evaluation indicators to minimize simulation training errors. After training, the network can accurately evaluate the key variables of the power grid under different load states, achieving analysis of the safety of the distribution network. The experimental results show that the proposed method can effectively capture key features in the input data, with an accuracy of 97.8% and a mean square error of 0.008, verifying the efficiency and accuracy of the proposed method. And this method can accurately evaluate the key variables of the power grid under different load states, with a keen perception ability for subtle changes, effectively improving the stability and safety of the power grid.