Smooth kinematic profiles are very important for high speed curve machining. During parametric interpolation, simple adaptive feedrate with confined contour error may cause acceleration and jerk to fluctuate acutely. To avoid the undesirable influence, an interpolation algorithm for parametric curves with smooth kinematic profiles is presented. The interpolator consists of three parts, look-ahead module, feedrate planning module and interpolation module. In look-ahead module, a pre-interpolator is designed to produce the required feedrate profile considering chord error. By feedrate planning, a smooth feedrate profile with confined acceleration and jerk is schemed based on bell-shape ACC/DEC profile by feedrate profile matching and feedrate profile synthesis. Then the parametric curve can be interpolated with the planned feedrate in interpolation module. Simulation results have been also provided to illustrate that the proposed interpolator can generate smooth kinematic profiles required for the high tracking accuracy at high speed with confined chord error, acceleration and jerk, and can be used for high speed and precision curve machining.