Breast cancer, as one of the main causes of death among women, has become a contentious study topic in the fields of clinical medicine and computer science. Mammography is a widely acknowledged procedure in the clinic for detecting early abnormalities in the breast, such as lumps and deformities that can progress to cancer. However, radiologists’ interpretation of the images is time-consuming and error-prone due to factors such as probable weariness. Medical imaging problems have benefited greatly from advances in deep learning approaches. We propose a deep transfer learning model for mammogram classification in this study. The findings are compared using Densenet-169, a deep convolutional neural network model with two alternative activation functions, Relu and Swish. First, we normalized the ROI images from the MIAS mammography database, which is freely available. Second, we used the augmentation method to avoid the problem of over-fitting. The augmented images are then integrated and trained with the proposed Densenet-169. During the training, both activation functions are used alternatively, and the classification accuracy of both models is compared. Densenet-169 with swish activation function could achieve better accuracy (91.72%) as compared to the same model with relu activation.