Abstract: For the generation of adaptive tetrahedral meshes, a new algorithm is presented to construct a three-dimensional size field taking the recursively subdivided regular grid, multi-grid, as the background grid. First, curvature adaptive mesh sizes are extracted from the geometric mesh controlled by refinement angle and global mesh size. Then, size constraint information is passed to the background grid using simplified size sources, and a regular grid is inserted into those cells where the element size requirement is much smaller than that of the current cell. Finally, a bi-directional progressive smoothing method is proposed to limit the size gradient. Various grid constructions such as regular grid, multi-grid are employed to represent the size distribution of a number of industrial models. The numerical examples show that multi-grid is superior in terms of element shape quality. Compared to regular grid, multi-grid required less time and about 14% memory to construct an almost identical gradient size field.