With the rapid development of modern power systems, power quality disturbances are a growing concern, impacting system reliability. Effective detection and identification of PQDs in new distribution systems with high renewable energy integration are crucial. In this paper, we propose a quantum-classical hybrid convolutional neural network for detecting and identifying power quality disturbances using a quantum-classical hybrid convolutional neural network (PQDs-QC-CNN). The PQDs-QC-CNN model includes quantum convolutional layers, fully connected layers, and softmax regression. The proposed PQDs-QC-CNN achieves a certain speed with the time complexity of \(O(\text {poly}(N))\) and the space complexity of O(N), where N is the number of qubits. Compared to classical convolutional neural networks, PQDs-QC-CNN leverages quantum algorithms, offering the advantage of lower computational complexity. According to the IEEE Std 1159-2019 standard, the experimental results of our PQDs-QC-CNN achieves 100% detection accuracy. Following the seven types of single disturbance signals, the identification is 99.25%. PQDs-QC-CNN represents a significant exploration of the application of quantum algorithms in the power system.