Breast cancer is the most frequent disease in women, with one in every 19 women at risk. Breast cancer is the fifth leading cause of cancer death in women around the world. The most effective and efficient technique of controlling cancer development is early identification. Mammography helps in the early detection of cancer, which saves lives. Many studies conducted various tests to categorize the tumor and obtained positive findings. However, there are certain limits. Mass categorization in mammography is still a problem, although it is critical in aiding radiologists in establishing correct diagnoses. The purpose of this study is to develop a unique hybrid technique to identify breast cancer mass pictures as benign or malignant. The combination of two networks helps accelerate the categorization process. This study proposes a novel-based hybrid approach, CNN-Inception-V4, based on the fusing of these two networks. Mass images are used in this research from the CBIS-DDSM dataset. 450 images are taken for benign, and 450 images are used for malignant. The images are first cleaned by removing pectoral muscles, labels, and white borders. Then, CLAHE is used to these images to improve their quality in order to produce promising classification results. Following preprocessing, our model classifies cancer in mammography pictures as benign or malignant abnormalities. Our proposed model’s accuracy is 99.2%, with sensitivity of 99.8%, specificity of 96.3%, and F1-score of 97%. We also compared our proposed model to CNN, Inception-V4, and ResNet-50. Our proposed model outperforms existing classification models, according to the results.