A novel algorithm for fitting surface reconstruction of unorganized data points is presented in this paper. Since the local geometric and topological properties can be clearly described with its neighboring points for a given point, the algorithm takes full advantage of this fact to generate a local triangular mesh based on Delaunay triangulation technique in two dimensions. The main contribution of the proposed algorithm is to progressively integrate those local triangular meshes into a resulting mesh by deleting the illegal triangles. In addition, holes and gaps can be detected automatically during reconstruction, and the algorithm works well for models with arbitrary topology. Experimental results show that this algorithm is effective, robust and can be easily implemented.