In this paper, a multi-stage progressive learning strategy is investigated to train classifiers for COVID-19 Diagnosis using imbalanced Chest Computed Tomography Data acquired from patients infected with COVID-19 Pneumonia, Community Acquired Pneumonia (CAP) and from normal healthy subjects. In the first learning stage, pre-processed volumetric CT data together with the segmented lung masks are fed into a 3D ResNet module, and an initial classification result can be obtained. However, due to categorical data imbalance, we observe large differences in sensitivity between COVID-19 and CAP cases. In the second stage, five learning models are independently trained over data with only COVID-19 and CAP cases, and are then ensembled to further discriminate the two classes. The final classification results are obtained by combining the predictions from both stages. Based on the validation dataset, we have evaluated our method and compared it with up-to-date methods in terms of overall accuracy and sensitivity for each class. The validation results validate the accuracy of the proposed multi-stage learning strategy. The overall accuracy of the validation dataset is 88.8%, and the sensitivities are 0.873, 0.789 and 1 for COVID-19, CAP and normal cases, respectively.