A new procedure is suggested for controlling the element size distribution of surface meshes during automatic adaptive surface mesh generation. In order to ensure that the geometry of the surface can be accurately captured, the curvature properties of the surface are first analyzed. Based on the principal curvatures and principal directions of the surface, the curvature element-size requirement is defined in form of a metric tensor field. This element-size controlling metric tensor field, which can either be isotopic or anisotopic depends on the user requirement, is then employed to control the element size distribution during mesh generation. The suggested procedure is local, adaptive and can be easily used with many parametric surface mesh generators. As the proposed scheme defines the curvature element-size requirement in an implicit manner, it can be combined with any other user defined element size specification using the standard metric intersection procedure. This eventually leads to a simple implementation procedure and a high computational efficiency. Numerical examples indicate that the new procedure can effectively control the element size of surface meshes in the cost of very little additional computational effort.