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Modern deep neural networks struggle to transfer knowledge and generalize across diverse domains when deployed to real-world applications. Currently, domain generalization (DG) is introduced to learn a universal representation from multiple domains to improve the network generalization ability on unseen domains. However, previous DG methods only focus on the data-level consistency scheme without considering the synergistic regularization among different consistency schemes. In this paper, we present a novel Hierarchical Consistency framework for Domain Generalization (HCDG) by integrating Extrinsic Consistency and Intrinsic Consistency synergistically. Particularly, for the Extrinsic Consistency, we leverage the knowledge across multiple source domains to enforce data-level consistency. To better enhance such consistency, we design a novel Amplitude Gaussian-mixing strategy into Fourier-based data augmentation called DomainUp. For the Intrinsic Consistency, we perform task-level consistency for the same instance under the dual-task scenario. We evaluate the proposed HCDG framework on two medical image segmentation tasks, i.e., optic cup/disc segmentation on fundus images and prostate MRI segmentation. Extensive experimental results manifest the effectiveness and versatility of our HCDG framework.