Federated Domain Generalization (FedDG) attempts to learn a global model in a privacy-preserving manner that generalizes well to new clients possibly with domain shift. Recent exploration mainly focuses on designing an unbiased training strategy within each individual domain. However, without the support of multi-domain data jointly in the mini-batch training, almost all methods cannot guarantee the generalization under domain shift. To overcome this problem, we propose a novel global objective incorporating a new variance reduction regularizer to encourage fairness. A novel FL-friendly method named Generalization Adjustment (GA) is proposed to optimize the above objective by dynamically calibrating the aggregation weights. The theoretical analysis of GA demonstrates the possibility to achieve a tighter generalization bound with an explicit re-weighted aggregation, substituting the implicit multi-domain data sharing that is only applicable to the conventional DG settings. Besides, the proposed algorithm is generic and can be combined with any local client training-based methods. Extensive experiments on several benchmark datasets have shown the effectiveness of the proposed method, with consistent improvements over several FedDG algorithms when used in combination. The source code is released at https://github.com/MediaBrain-SJTU/FedDG-GA.