Entity alignment (EA) aims to identify the same real-world entities presented in different knowledge graphs (KGs), which is the most crucial step in integrating multi-source KGs. Existing entity alignment methods based on Graph Neural Networks mainly focus on aggregating neighborhood structure information within the original graph to generate entity embeddings. However, these methods fail to effectively leverage the global structural information of entities. In this paper, we propose a novel method based on Global Structure-Aware Graph Neural Networks to capture the global structure between entities. Specifically, our method learns global embeddings from the augmented graph reconstructed by Singular Value Decomposition. Moreover, we employ contrastive learning to maximize the consistency between global and local embeddings while mitigating the over-smoothing problem. Extensive experimental results on benchmark datasets, along with further analysis, demonstrate the superiority and effectiveness of our method. The source code is available at https://github.com/wonderCS1213/GSEA .