The World Health Organization states that early diagnosis is essential to increasing the cure rate for breast cancer, which poses a danger to women's health worldwide. However, the efficacy and cost limitations of conventional diagnostic techniques increase the possibility of misdiagnosis. In this work, we present a quantum hybrid classical convolutional neural network (QCCNN) based breast cancer diagnosis approach with the goal of utilizing quantum computing's high-dimensional data processing power and parallelism to increase diagnosis efficiency and accuracy. When working with large-scale and complicated datasets, classical convolutional neural network (CNN) and other machine learning techniques generally demand a large amount of computational resources and time. Their restricted capacity for generalization makes it challenging to maintain consistent performance across multiple data sets. To address these issues, this paper adds a quantum convolutional layer to the classical convolutional neural network to take advantage of quantum computing to improve learning efficiency and processing speed. Simulation experiments on three breast cancer datasets, GBSG, SEER and WDBC, validate the robustness and generalization of QCCNN and significantly outperform CNN and logistic regression models in classification accuracy. This study not only provides a novel method for breast cancer diagnosis but also achieves a breakthrough in breast cancer diagnosis and promotes the development of medical diagnostic technology.