In this paper, we propose a new NURBS modeling technique, called NURBS fusion and present a complete algorithm for NURBS fusion. Working on a set of intersecting NURBS surfaces, NURBS fusion automatically eliminates the intersected parts and connects the remaining parts smoothly with auxiliary surfaces, so that a polysurface composed of multiple nicely joined NURBS patches is obtained. The surface fusion algorithm performs in three steps. First, surface/surface intersection is computed by a subdivision based algorithm, which gives intersecting point pairs in parameter domains. Second, base surfaces are trimmed "excessively" along intersection curves to eliminate the intersected parts and make gaps that will be filled by the auxiliary connection surfaces. Finally, bicubic B-spline auxiliary surfaces are constructed to connect the base surfaces in a smooth fashion. Our algorithm is concise, fast, and it produces low degree NURBS results compatible with most data-exchange standards.