Abstract: To reconstruct surface from noisy point clouds, a surface reconstruction algorithm based on Delaunay refinement was proposed. Firstly, the local surface was approximated by algebraic sphere, which was fitted through neighbor point coordinates and normals by robust least square algorithm. Compared with traditional sphere fitting methods, the new method is more robust to noises and outliers. Secondly, to find any segment intersect with surface for Delaunay refinement procedure, the surface bounding spheres intersected with segment were efficiently founded with AABB-tree. Then, initialized with sphere center, the first approximated segment-surface intersections within bounding spheres were parallel-computed by iterative segment-sphere intersection. Finally, the surface was meshed by Delaunay refinement, which is not ambiguous and can reconstruct surface with good aspect ratio comparing with Marching-cube algorithm. Experiments show that the new algorithm can efficiently, robustly and accurately reconstruct surface from point clouds with high noises. But its time and memory consuming will rapidly increase for precise models.