We propose a novel graph rank-based average pooling neural network (GRAPNN) to detect secondary pulmonary tuberculosis patients via chest CT imaging. (Methods) First, we propose a novel rank-based pooling neural network (RAPNN) to learn the individual image-level features from chest CT images. Second, we integrate the graph convolutional network (GCN), which learns relation-aware representation among the batch of chest CT images, to RAPNN.Third, we build a novel Graph RAPNN (GRAPNN) model based on the previous integration via k-means clustering and knearest neighbors' algorithm. Besides, an improved data augmentation is utilized to handle overfitting problem. Grad-ACM is used to make this GRAPNN model explainable. (Results) This proposed GRAPNN method is compared with seven stateof-the-art algorithms. The results showed GRAPNN model yields the best performances with a sensitivity of 94.65%, a specificity of 95.12%, a precision of 95.17%, an accuracy of 94.88%, and an F1 score of 94.87%. (Conclusions) Our GRAPNN is superior to other seven state-of-the-art approaches. The explainable mechanism in our method can identify the lesions of important lung parts (tuberculosis cavities and surrounding small lesions) for transparent decision.