Abstract: This paper presents an algorithm for simultaneously fitting smoothly connected multiple surfaces from unorganized measured data. A hybrid mathematical model of B-spline surfaces and Catmull-Clark subdivision surfaces is introduced to represent objects with general quadrilateral topology. The interconnected multiple surfaces are G² continuous across all surface boundaries except at a finite number of extraordinary corner points where G¹ continuity is obtained. The algorithm is purely a linear least-squares fitting procedure without any constraint for maintaining the required geometric continuity. In case of general uniform knots for all surfaces, the final fitted multiple surfaces can also be exported as a set of Catmull-Clark subdivision surfaces with global C² continuity and local C¹ continuity at extraordinary corner points.