To enhance the classification accuracy of power quality disturbance signals (PQDs) in the presence of noise and abnormal data interference, this paper introduces a dual-branch parallel feature fusion network-based classification method. First, feature extraction of two branches is accomplished by using a one-dimensional residual neural network and a one-dimensional convolutional neural network. Then, these extracted features are fused together through a feature fusion module. Finally, a classification module is used to accurately classify PQDs. In contrast to serial neural networks, this approach combines feature vectors enhancing feature distinctiveness and is compatible with parallel computing, further improving recognition speed. Simulation results demonstrate that this method achieves recognition rates exceeding 95% for PQDs classification tasks with signal-to-noise ratios of 13 dB, 15 dB, and 18 dB. Additionally, the method exhibits a certain level of robustness in classifying abnormal data.