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Zero-shot learning (ZSL) aims to leverage additional semantic information to recognize unseen classes. To transfer knowledge from seen to unseen classes, most ZSL methods often learn a shared embedding space by simply aligning visual embeddings with semantic prototypes. However, methods trained under this paradigm often struggle to learn robust embedding space because they align the two modalities in an isolated manner among classes, which ignore the crucial class relationship during the alignment process. To address the aforementioned challenges, this paper proposes a Visual-Semantic Graph Matching Net, termed as VSGMN, which leverages semantic relationships among classes to aid in visual-semantic embedding. VSGMN employs a Graph Build Network (GBN) and a Graph Matching Network (GMN) to achieve two-stage visual-semantic alignment. Specifically, GBN first utilizes an embedding-based approach to build visual and semantic graphs in the semantic space and align the embedding with its prototype for first-stage alignment. Additionally, to supplement unseen class relations in these graphs, GBN also build the unseen class nodes based on semantic relationships. In the second stage, GMN continuously integrates neighbor and cross-graph information into the constructed graph nodes, and aligns the node relationships between the two graphs under the class relationship constraint. Extensive experiments on three benchmark datasets demonstrate that VSGMN achieves superior performance in both conventional and generalized ZSL scenarios. The implementation of our VSGMN and experimental results are available at github: https://github.com/dbwfd/VSGMN