An efficient real-time Non-Uniform Rational B-Spline (NURBS) curve interpolator for high-speed and high-accuracy curve machining is developed and implemented, which considers the confined contour error, acceleration/deceleration (ACC/DEC) planning and the machine dynamic response simultaneously. A practical method is proposed to adjust the feed rate to the curvature radius of NURBS curves to achieve higher machining precision. However, at the sharp corner of the curves, the feed rate fluctuation might result in large impacts to machine tools. The offline pre-interpolation for sharp corners is presented. The feed rate is reduced in advance according with the machine's acceleration capability as well as satisfying the confined contour error. The velocity profile can be chosen dynamically to meet the requirements of the machining process by means of flexible ACC/DEC planning. In addition, a new strategy based on the geometrical properties of NURBS curves is suggested to predict the deceleration point. Therefore, the process of acceleration and deceleration is so smooth that it can satisfy the need of the machining process. This NURBS interpolator has been validated on a CNC system, which greatly improves machining accuracy for both position and velocity control.