Fairness-aware domain generalization (FairDG) has emerged as a critical challenge for deploying trustworthy AI systems, particularly in scenarios involving distribution shifts. Traditional methods for addressing fairness have failed in domain generalization due to their lack of consideration for distribution shifts. Although disentanglement has been used to tackle FairDG, it is limited by its strong assumptions. To overcome these limitations, we propose Fairness-aware Classifier-Guided Score-based Diffusion Models (FADE) as a novel approach to effectively address the FairDG issue. Specifically, we first pre-train a score-based diffusion model (SDM) and two classifiers to equip the model with strong generalization capabilities across different domains. Then, we guide the SDM using these pre-trained classifiers to effectively eliminate sensitive information from the generated data. Finally, the generated fair data is used to train downstream classifiers, ensuring robust performance under new data distributions. Extensive experiments on three real-world datasets demonstrate that FADE not only enhances fairness but also improves accuracy in the presence of distribution shifts. Additionally, FADE outperforms existing methods in achieving the best accuracy-fairness trade-offs.