Open-world few-shot classification is restricted by inadequate image-level content representation capabilities when the training and testing sets have significant differences in categories. Recently, many studies show the effectiveness of deep local descriptor-based methods, which attempt to select out dominating contents and discard noisy ones. However, aforementioned methods focus more on external relevance of support and query sets to filter features and ignore internal relevance among support sets, leading to unsatisfying classification performance. To relieve the issue, in this article, we propose the complementary learning Decoupling Category-Region-Aware Network (DCRNet) to simultaneously learn the correlation between internal members and then interact with the external sets. Specifically, we first propose an effective learnable Category Prototype-generated Feature Decoupling Module (CPFDM) to mine co-existing representations and generate comprehensive global class prototype. Then, to adaptively filter out discriminative local descriptors, we present a Category-Aware Selection Module (CASM) and introduce the Category-Aware Contrastive Loss (CACL) to highlight local information that is highly relative to the current category. In addition, the Region-Aware Contrastive Loss (RACL) is designed to encourage the model to concentrate on local regions, yielding powerful ability to distinguish foreground regions from between various categories. Finally, we leverage the filtered support descriptors to adaptively refine query descriptors through the descriptor selection strategy. Extensive experiments demonstrate that the proposed solution outperforms state-of-the-arts on five mainstream general and fine-grained few-shot classification datasets. We have released the training and testing code on https://github.com/jjfang007/DCRNet .