The key of Weakly Supervised Fine-grained Image Classification (WFGIC) is how to pick out the discriminative regions and learn the discriminative features from them. However, most recent WFGIC methods pick out the discriminative regions independently and utilize their features directly, while neglecting the facts that regions' features are mutually semantic correlated and region groups can be more discriminative. To address these issues, we propose an end-to-end Graph-propagation based Correlation Learning (GCL) model to fully mine and exploit the discriminative potentials of region correlations for WFGIC. Specifically, in discriminative region localization phase, a Criss-cross Graph Propagation (CGP) sub-network is proposed to learn region correlations, which establishes correlation between regions and then enhances each region by weighted aggregating other regions in a criss-cross way. By this means each region's representation encodes the global image-level context and local spatial context simultaneously, thus the network is guided to implicitly discover the more powerful discriminative region groups for WFGIC. In discriminative feature representation phase, the Correlation Feature Strengthening (CFS) sub-network is proposed to explore the internal semantic correlation among discriminative patches' feature vectors, to improve their discriminative power by iteratively enhancing informative elements while suppressing the useless ones. Extensive experiments demonstrate the effectiveness of proposed CGP and CFS sub-networks, and show that the GCL model achieves better performance both in accuracy and efficiency.