In this work we develop a computer-aided diagnosis (CAD) scheme for classification of pulmonary disease for grating-based x-ray radiography. In addition to conventional transmission radiography, the grating-based technique provides a dark-field imaging modality, which utilizes the scattering properties of the x-rays. This modality has shown great potential for diagnosing early stage emphysema and fibrosis in mouse lungs in vivo. The CAD scheme is developed to assist radiologists and other medical experts to develop new diagnostic methods when evaluating grating-based images. The scheme consists of three stages: (i) automatic lung segmentation; (ii) feature extraction from lung shape and dark-field image intensities; (iii) classification between healthy, emphysema and fibrosis lungs. A study of 102 mice was conducted with 34 healthy, 52 emphysema and 16 fibrosis subjects. Each image was manually annotated to build an experimental dataset. System performance was assessed by: (i) determining the quality of the segmentations; (ii) validating emphysema and fibrosis recognition by a linear support vector machine using leave-one-out cross-validation. In terms of segmentation quality, we obtained an overlap percentage (Ω) 92.63 ± 3.65%, Dice Similarity Coefficient (DSC) 89.74 ± 8.84% and Jaccard Similarity Coefficient 82.39 ± 12.62%. For classification, the accuracy, sensitivity and specificity of diseased lung recognition was 100%. Classification between emphysema and fibrosis resulted in an accuracy of 93%, whilst the sensitivity was 94% and specificity 88%. In addition to the automatic classification of lungs, deviation maps created by the CAD scheme provide a visual aid for medical experts to further assess the severity of pulmonary disease in the lung, and highlights regions affected.