Skinning or lofting remains a challenging problem in computer graphics and free-form surface design. Although it was addressed by many researchers, no sufficiently general solution has been proposed yet. In the interpolating approach, the incompatibility of the input NURBS curves are solved by knot insertion. This process leads to an explosion in the number of control points defining the skinned surface. Other methods avoid this problem by generating skinned surfaces that approximate rather than interpolate the input curves. In this paper, we provide a solution to this problem using T-splines. Compared with existing approaches, a T-spline skinned surface interpolates a set of incompatible curves with a control mesh of fewer vertices. Typically, the linear system involved could be solved globally. However, our approach provides a local solution for each skinned curve. As such, local modification could be used to meet additional constraints such as given normal and/or predefined curvature across the skinned curves.