In recent years, significant advances in gait recognition have been seen, with many methods reporting high accuracy on certain datasets. However, domain shifts, such as distribution inconsistencies in viewpoint or clothing, can severely degrade the performance of these models on unseen target domains, hindering the widespread application of gait recognition. Some unsupervised domain adaptation (UDA) methods have been proposed to address this problem. However, these approaches require continual updates with target domain data, which is often difficult to obtain due to privacy concerns and deployment complexity. This paper presents GaitDG, a single-source domain generalization framework designed to enhance the generalization ability of gait recognition models for unseen target domains, requiring training on only one source domain without accessing target domain data. During training, GaitDG employs adversarial training to disentangle domain-specific and identity-specific features, enabling the discovery of latent sub-domains and the extraction of domain-invariant features. Furthermore, GaitDG supports the integration of data augmentation to diversify the source domain data. We also introduce a data augmentation method, Segmentation Model Transfer (SMT), to mitigate recognition performance degradation caused by variations in segmentation models. As a model-agnostic approach, GaitDG can directly enhance the cross-domain recognition performance of gait recognition models without altering their structure. Comprehensive experiments on widely used gait datasets demonstrate that GaitDG significantly improves the cross-domain recognition performance of several state-of-the-art gait recognition models.