Mammography screening is one of the common techniques that help identify suspicious masses' malignancy of breast cancer at an early stage. Yet, the early diagnosis of masses in mammograms is still challenging for dense and extremely dense breast categories and requires efficient and automated systems to assist radiologists in their diagnosis. Deep learning methods have widely been used for medical imaging applications, especially for breast masses classification. A novel capsule concept has recently been proposed to solve the drawbacks of deep learning models based on classic convolutional networks by learning the hierarchical structures in images. However, the originally proposed capsule network suffers from issues due to high number of parameters and high computational time. This paper proposes a new architecture of the capsule network that significantly reduces the computational time of the original capsule network by 6.5 times and makes the training of breast masses ROIs on affordable GPUs possible. The proposed architecture was fine-tuned according to the number of kernels and capsules and by using data augmentation. The results of the evaluation of the four breast density categories show that our capsule-based model outperforms existing techniques in classifying suspicious breast masses in one stage. The binary classification of masses into normal and abnormal achieves an accuracy of 96.03%, a F1-score of 96.27%, a precision of 94.28%, a recall of 98.38%, a specificity of 93.97%, and an AUC of 0.997. The multi-classification of breast masses into normal, benign, and malignant scores an accuracy of 77.78%, a F1-score of 77.45%, a precision of 71.54%, a recall of 84.54%, a specificity of 83.15%, and an AUC of 0.9.