Lightning disturbance may be misjudged as dc fault by the primary protection in the flexible high voltage dc (HVDC) grid. To solve this problem, an auxiliary fault identification strategy based on convolutional neural network with branch structures (BR-CNN) is proposed in this paper. In the proposed scheme, the voltage and current characteristic matrix is constructed as the input matrix of BR-CNN model and the output categories include positive pole-to-ground (PTG) fault and lightning disturbance. Voltage and current branches are constructed to extract high-level local features of input data layer by layer, and main branch is designed to realize the comprehensive utilization of voltage and current information. Through autonomous learning of the model, the nonlinear mapping relationship between input and output is constructed. The method only uses the single-terminal quantities, and can be used as an auxiliary criterion to improve the reliability of the primary protection. The test results verify the effectiveness of the method, and the recognition accuracy is better than the traditional classification models.