We introduce a novel technique for surface reconstruction from unorganized points by applying Kohonen's self-organizing map. The topology of the surface is predetermined, and a neural network learning algorithm is carried out to obtain correct 3D coordinates at each vertex of the surface. Edge swap and multiresolution learning are proposed to make the algorithm more effective and more efficient. The whole algorithm is very simple to implement. Experimental results have shown our techniques are successful.Paper postscript and pdf files as it appears in IEEE Visualization'99 Late Breaking Hot Topics.