Abstract: The NURBS (non-uniform rational B-spline) interpolator was studied with the first and second order Taylor expansion to approximate NURBS parameter. Numerical example results proved that the interpolation velocity is almost the same to reference velocity. The relationships between curvature and velocity fluctuating and between chord error and interpolation period in the Taylor expansion were given. It was found that the NURBS interpolator with Taylor expansion is actually a kind of open loop method. However, it ignores the output capability of a mechanical system and, therefore, big processing error may occur when the output capability of the mechanical system is insufficient.