Abstract: The ball-vertex method can effectively avoid the occurrence of invalid elements.However, it is less efficient.In order to overcome this problem, the vertex-ball spring smoothing method is proposed.Following the basic Laplacian mesh smoothing concept, the sub-mesh systems based on the"ball-vertex"model are constructed and solved iteratively by a LDL^T solver.Interior nodes are smoothed layer by layer in an effective manner to achieve the mesh deformations.It can be applied not only to 2D/3D dynamic mesh, but also to the hybrid mesh.Numerical examples show that the method proposed is robust for substantially distorted mesh and the efficiency is significantly improved.It is suitable for large-scale dynamic problems with large deformations.