LiDAR-based Vehicle-to-Everything (V2X) cooperative perception has demonstrated its impact on the safety and effectiveness of autonomous driving. Since current cooperative perception algorithms are trained and tested on the same dataset, the generalization ability of cooperative perception systems remains underexplored. This paper is the first work to study the Domain Generalization problem of LiDAR-based V2X cooperative perception (V2X-DG) for 3D detection based on four widely-used open source datasets: OPV2V, V2XSet, V2V4Real and DAIR-V2X. Our research seeks to sustain high performance not only within the source domain but also across other unseen domains, achieved solely through training on source domain. To this end, we propose Cooperative Mixup Augmentation based Generalization (CMAG) to improve the model generalization capability by simulating the unseen cooperation, which is designed compactly for the domain gaps in cooperative perception. Furthermore, we propose a constraint for the regularization of the robust generalized feature representation learning: Cooperation Feature Consistency (CFC), which aligns the intermediately fused features of the generalized cooperation by CMAG and the early fused features of the original cooperation in source domain. Extensive experiments demonstrate that our approach achieves significant performance gains when generalizing to other unseen datasets while it also maintains strong performance on the source dataset.