Digital breast tomosynthesis (DBT) is a pseudo-three-dimensional x-ray imaging modality proposed to decrease the effect of tissue superposition present in mammography, potentially resulting in an increase in clinical performance for the detection and diagnosis of breast cancer. Tissue classification in DBT images can be useful in risk assessment, computer-aided detection and radiation dosimetry, among other aspects. However, classifying breast tissue in DBT is a challenging problem because DBT images include complicated structures, image noise, and out-of-plane artifacts due to limited angular tomographic sampling. In this project, we propose an automatic method to classify fatty and glandular tissue in DBT images. First, the DBT images are pre-processed to enhance the tissue structures and to decrease image noise and artifacts. Second, a global smooth filter based on L0 gradient minimization is applied to eliminate detailed structures and enhance large-scale ones. Third, the similar structure regions are extracted and labeled by fuzzy C-means (FCM) classification. At the same time, the texture features are also calculated. Finally, each region is classified into different tissue types based on both intensity and texture features. The proposed method is validated using five patient DBT images using manual segmentation as the gold standard. The Dice scores and the confusion matrix are utilized to evaluate the classified results. The evaluation results demonstrated the feasibility of the proposed method for classifying breast glandular and fat tissue on DBT images.