Abstract: Surface fitting from curves is a basic problem in CAGD.However,the existing algorithms cannot control the fitted error between the fitted surface and the input curves.In order to solve this problem,a new algorithm is proposed to construct a B-spline surface by fitting four boundary curves and a set of unorganized curves.The approach first constructs a base surface from the boundary curves,and then subdivides the surface and input curves into Bézier form.Borrowing the idea from surface skinning,the algorithm obtains the linear equation system with C¹ continuity constraint about the surface to be fitted.Then we use SVD and energy minimization to obtain the fitted surface.The new knots will be inserted into the surface where the distance is larger than the error until the distance is small enough.Several experimental results demonstrate that the proposed algorithm is more numerical stable than the previous methods,and can generate smooth surface whose fitted error is smaller than the user specified tolerance.