Normal mesh is a new fundamental surface descrip-tion, which is multiresolution mesh where each level can be written as a normal offset from a coarser version. In this paper, we present an algorithm to create normal subdivision triangulations approxi-mating implicit surfaces. Our algorithm begins from a coarse base mesh created by a space-division based polygonization method for implicit surface, and the base mesh is then optimized by Laplacian smoothing operator. Subsequently, the faces of the base mesh are subdivided iteratively and the newly created vertices are located on the implicit surface along a certain direction, which depends on the normals of vertices of the faces. Finally, we obtain a piecewise-linear appro-ximation of the surface, which is a normal mesh with subdivision connectivity and provides a multi-resolution description of the implicit surface naturally. Under the same error restriction, the mesh has much fewer data with respect to the traditional polygoniza-tion algorithms.