The original Poisson surface reconstruction algorithm can easily produce an unclosed surface at the edge, resulting in the surface of the final object being rough with holes. This paper proposes an improved three-dimensional algorithm for reconstructing surfaces from point clouds. First, the method employs a statistical filter to simplify the denoising of the considered point clouds and eliminates the jagged phenomenon of the reconstructed surface. Then, a topological structure of point clouds is established, and the point-cloud normal vector is normally redirected to reduce the ambiguity of the normal direction. Finally, the point cloud with the disk topological structure is mapped to the plane, the two-dimensional triangulation method is applied to the plane parameterization, the triangle connectivity is provided to the two-dimensional points, and the two-dimensional points are transmitted back to the three-dimensional point cloud to form a mesh surface. The experimental results demonstrate that the method can effectively remove noise points, construct a more regular triangle mesh, and effectively remove the pseudo-enclosed surface. The surface point-cloud reconstruction effect with holes is clearly improved, and the reconstruction time is reduced.