The method of reconstructing NURBS surface with features is proposed in this paper. Features including boundary curves and feature points are recognized from the scanned data. An initial surface is constructed with boundary curves. The desired NURBS is determined by modifying the initial surface to pass through feature points. Lagrange multiplier is used to find the solution. The error analysis is then done. Examples are given to verify the algorithm at last. The method can keep some features fixed and be widely used in CAD modeling.