Abstract: A systematic study on computing the integral curvature line on NURBS surface is presented. Discrete normal is used to simplify calculation of the second fundamental form of the surface,resulting in accelerating the Euler iteration process in solving the differential equation of curvature line.Discrete points on the curvature line are then obtained and approximated by an explicitly presented B-spline curve on the NURBS surface using singular mixed interpolation and capable of controlling the error within a given tolerance. The proposed approach helps to promote the application and popularization of curvature line in CAGD and surface modeling.