Abstract. In this paper, we first investigate the integral curvature condition to extend the mean curvature flow of submanifolds in a Riemannian manifold with codimension d  1, which generalizes the extension theorem for the mean
curvature flow of hypersurfaces due to Le-ˇ Seˇsum [12] and the authors [25, 26]. Using the extension theorem, we prove two convergence theorems for the mean curvature flow of closed submanifolds in Rn+d under suitable integral curvature conditions.