Out-of-distribution (OOD) generalization is an important issue for Graph Neural Networks (GNNs). Recent works employ different graph editions to generate augmented environments and learn an invariant GNN for generalization. However, the graph structural edition inevitably alters the graph label. This causes the label shift in augmentations and brings inconsistent predictive relationships among augmented environments. To address this issue, we propose LiSA, which generates label-invariant augmentations to facilitate graph OOD generalization. Instead of resorting to graph editions, LiSA exploits Label-invariant Subgraphs of the training graphs to construct Augmented environments. Specifically, LiSA first designs the variational subgraph generators to efficiently extract locally predictive patterns and construct multiple label-invariant subgraphs. Then, the subgraphs produced by different generators are collected to build different augmented environments. To promote diversity among augmented environments, LiSA further introduces a tractable energy-based regularization to enlarge pair-wise distances between the distributions of environments. In this manner, LiSA generates diverse augmented environments with a consistent predictive relationship to facilitate learning an invariant GNN. Extensive experiments on node-level and graph-level OOD benchmarks show that LiSA achieves impressive generalization performance with different GNN backbones. Code is available on https://github.com/Samyu0304/LiSA.