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Domain adaptation aims to exploit a label-rich source domain for learning classifiers in a different label-scarce target domain. It is particularly challenging when there are significant divergences between the two domains. In the paper, we propose a novel unsupervised domain adaptation method based on progressive domain augmentation. The proposed method generates virtual intermediate domains via domain interpolation, progressively augments the source domain and bridges the source-target domain divergence by conducting multiple subspace alignment on the Grassmann manifold. We conduct experiments on multiple domain adaptation tasks and the results shows the proposed method achieves the state-of-the-art performance.