Improvement of the quality of surface meshes is important for mesh generation and numerical simulation. The challenge with surface mesh improvement is to improve element quality while preserving the surface characteristics as much as possible. A procedure is presented here to optimize the quality of elements in surface meshes by node repositioning while keeping the nodes on the original mesh faces and close to their original locations. The nodes are repositioned in a series of local parametric spaces derived from individual mesh elements rather than a global parametric space constructed from the complete mesh. The local parametric spaces are derived from barycentric mapping of triangles and isoparametric mapping of quadrilaterals. The procedure has been tested successfully on a number of complex triangular and quadrilateral meshes. Quantitative measures are presented to prove that the mesh quality is improved and the deviation of the optimized mesh from the original mesh is small.