Abstract: To avoid the generation of low-quality elements in regions where abrupt changes of element sizes are defined, a nonlinear programming problem(NLP) is formulated to help smooth the sizing function defined on an unstructured background mesh, and a geometry-based adaptive tetrahedral mesh generation algorithm is thus set up with this novel element-sizing smoothing algorithm as one of the key ingredients. The proposed algorithm inputs a valid and closed CAD model and creates an unstructured background mesh to cover the problem domain defined by this CAD model. Then, an initial sizing function can be set up by calculating a sizing value at each background mesh node. Note that this size value is adapted to the curvature and proximity features of the CAD model. After that, a convex NLP is solved to smooth this sizing function such that the changes of element scales are under control. By using the smoothed sizing function to control the distributions of element scales, high-quality surface and volume meshes can finally be produced on the surface and interior of the CAD model, respectively. Numerical experiments show that, the proposed algorithm can be executed in a fully automatic fashion, and the user could manipulate the results of this algo-rithm through five global user parameters.