Feature location and extraction play important roles in ground-based cloud classification. However, popular cloud classification algorithms have a low classification performance because they widely use hand-crafted features which require accurate manual labeling. In addition, most of deep learning algorithms cannot capture accurate salient features in cloud images which is useful to ground-based cloud classification. In this study, a weakly supervised ground-based cloud classification method (WS-GCCA) is proposed based on the global and local features extracted by a coarse-grained and a fine-grained deep networks. The performance of the WS-GCCA is validated with a ground-based cloud classification database comprising 11 cloud types. Experimental results demonstrate that the proposed WS-GCCA achieves an accuracy of 98.58, which is significantly higher classification accuracy than 10 state-of-art supervised learning algorithms.