The idea of velocity field control has recently been used to tackle contour following problems. Although promising results have been reported in previous studies, the contour to be followed used in those studies were not represented in the form of Non-uniform rational B-Spline (NURBS), which is the fundamental geometric representation in many CAD/CAM systems. In order to extend velocity field control to contours represented in NURBS form, this paper develops a novel approach that constructs the velocity fields at preselected grid points. For any point not on the desired contour, its associated velocity field can be calculated in real-time using a simple interpolation formula and the velocity fields at nearby grid points. Several contour following experiments were conducted with a two-link robot to demonstrate the effectiveness of the proposed approach. Experimental results indicate that the proposed approach is feasible.