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Knowledge graph completion (KGC) aims at completing missing information in knowledge graphs (KGs). Most previous works work well in the transductive setting, but are not applicable in the inductive setting, i.e., test entities can be unseen during training. Recently proposed methods obtain inductive ability by learning logic rules from subgraphs. However, all these works only consider the structural information of subgraphs while ignoring the rich contextual semantic information underlying KGs, which tends to lead to a sub-optimal embedding result. Furthermore, they tend to perform poorly when the subgraphs are sparse. To address these problems, we propose a global and local Con text- e nhanced E mbedding network, ConeE, which can fully utilize local and global contextual information to enhance embedding representations through the following two components. (1) The global context modeling module (GCMM) is a semi-parametric coarse-grained global semantic extractor, which can effectively extract global context-based semantic information via a BERT-based context encoder and a semantic fusion network (SFN), and adopts a novel contrastive learning-based sampling strategy to optimize semantic features. Furthermore, a scoring network is designed to evaluate the confidence of triplets from the perspective of both the triplet facts and the reasoning path to improve the accuracy of prediction. (2) The local context modeling module (LCMM) employs an interactive graph neural network (IGNN) to extract local topological features from subgraphs, and applies mutual information maximization (MIM) to subgraph modeling to capture more local features. Experiments on benchmark datasets show that ConeE significantly outperforms existing state-of-the-art methods. • A multi-granular contextual semantic enhancement method is proposed. • ConeE can fully capture global and local semantic features via GCMM and LCMM. • ConeE can make full use of the induction ability of GNN via IGNN. • Our proposed model achieves SOTA performance on multiple benchmark datasets. [ABSTRACT FROM AUTHOR]