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.