Abstract: This paper deals with the problem of reconstructing algebraic surfaces over triangular meshes. Firstly,a quadratic surface and a plane are constructed over every edge of triangle.Their intersection is the edge curve.Secondly,we divide the triangle into three parts and define three cubic surfaces over every part. These cubic surfaces not only intersect smoothly along there intersection curves,but also meet with quadratic surfaces GC¹ continuity.Then a GC¹ continuous surface is gotten over the whole triangular meshes.