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COVID-19 is spreading rapidly around the world. In order to diagnose it quickly and accurately and thus block the chain of epidemic transmission, the study proposed a deep learning-based classification network DLDA-A-DenseNet. Firstly, DenseNet-201 combined deep layer dense aggregation to aggregate feature information at different stages to enhance its ability to identify and localize lesions. Secondly, this paper proposed efficient multi-scale long-range attention to refine the aggregated features. Moreover, this paper used a balanced sampling training strategy to eliminate the bias for the class imbalance problem of CT image dataset. Testing on the China consortium of chest CT image investigation dataset, the method improved 2.24%,3.09%,2.09%,2.60% and 3.48% in accuracy, recall, precision, F1 score and Kappa coefficient compared with DenseNet-201,and achieved an optimal accuracy of 99.50% on COVID-CISet image dataset. The results show that the proposed COVID-19 CT image classification method can fully extract the lesion features of CT slices compared with other methods, and has higher classification accuracy and good generalizability. [ABSTRACT FROM AUTHOR]