Background and Objective: Many developed and non-developed countries worldwide suffer from cancer-related fatal diseases. In particular, the rate of breast cancer in females increases daily, partially due to unawareness and undiagnosed at the early stages. A proper first breast cancer treatment can only be provided by adequately detecting and classifying cancer during the very early stages of its development. The use of medical image analysis techniques and computer-aided diagnosis may help the acceleration and the automation of both cancer detection and classification by also training and aiding less experienced physicians. For large datasets of medical images, convolutional neural networks play a significant role in detecting and classifying cancer effectively. Methods: This article presents a novel computer-aided diagnosis method for breast cancer classification (both binary and multi-class), using a combination of deep neural networks (ResNet 18, ShuffleNet, and Inception-V3Net) and transfer learning on the BreakHis publicly available dataset. Results and Conclusions: Our proposed method provides the best average accuracy for binary classification of benign or malignant cancer cases of 99.7%, 97.66%, and 96.94% for ResNet, InceptionV3Net, and ShuffleNet, respectively. Average accuracies for multi-class classification were 97.81%, 96.07%, and 95.79% for ResNet, Inception-V3Net, and ShuffleNet, respectively.