An improvement on the Delaunay graph mapping dynamic gird method based on radial basis function interpolation is presented in this paper to enhance the efficiency and quality of dynamic grid generation. First, the displacements of far-field background grid nodes are calculated by means of radial basis function interpolation with polynomial terms, and then the displacements of computational grid nodes are acquired with the interpolation of background grid nodes displacements. Finally, the displacements of the far-field computational grid nodes are decreased to zero with the use of damp functions. Differences between the improved method and the original Delaunay graph mapping method are investigated based on a grid deformation example of rectangle rotation. The effect of the number of radial basis functions'center points and damp functions on deformed grid quality are also investigated. The grid deformation for rectangle rotation shows that the improved method can accurately recover the rotation of the Delaunay background grid. Dynamic grid generation for NACA 0012 airfoil, NLR 7301 bi-element airfoil and M6 wing further demonstrates that with the insertion of control points the improved method can generate high quality dynamic grids for large deformation without the regeneration of the background grid.