Precise classification of pulmonary textures is crucial to develop a computer aided diagnosis (CAD) system of diffuse lung diseases (DLDs). Although deep learning techniques have been applied to this task, the classification performance is not satisfied for clinical requirements, since commonly-used deep networks built by stacking convolutional blocks are not able to learn discriminative feature representation to distinguish complex pulmonary textures. For addressing this problem, we design a multi-scale attention network (MSAN) architecture comprised by several stacked residual attention modules followed by a multi-scale fusion module. Our deep network can not only exploit powerful information on different scales but also automatically select optimal features for more discriminative feature representation. Besides, we develop visualization techniques to make the proposed deep model transparent for humans. The proposed method is evaluated by using a large dataset. Experimental results show that our method has achieved the average classification accuracy of 94.78% and the average f-value of 0.9475 in the classification of 7 categories of pulmonary textures. Besides, visualization results intuitively explain the working behavior of the deep network. The proposed method has achieved the state-of-the-art performance to classify pulmonary textures on high resolution CT images.