Domain adaptation in the Euclidean space is a challenging task on which researchers recently have made great progress. However, in practice, there are rich data representations that are not Euclidean. For example, many high-dimensional data in computer vision are in general modeled by a low-dimensional manifold. This prompts the demand of exploring domain adaptation between non-Euclidean manifold spaces. This article is concerned with domain adaption over the classic Grassmann manifolds. An optimal transport-based domain adaptation model on Grassmann manifolds has been proposed. The model implements the adaption between datasets by minimizing the Wasserstein distances between the projected source data and the target data on Grassmann manifolds. Four regularization terms are introduced to keep task-related consistency in the adaptation process. Furthermore, to reduce the computational cost, a simplified model preserving the necessary adaption property and its efficient algorithm is proposed and tested. The experiments on several publicly available datasets prove the proposed model outperforms several relevant baseline domain adaptation methods.