The development of motion control enables robot manipulators to reproduce the humans motion as known as motion-copying system. This epochal system is expected to automate delicate tasks that has been treated by human workers. Moreover, the motion-copying system can reproduce the stored motion at high speed by scaling time-axis of the stored motion-data. Using this technique, the efficiency of the industry will be substantially improved. However, there are still some problems that obstruct the practical use of the high speed motion-reproduction. One of the serious problem is how to change the reproduction speed. Although the most simple method is varying the sampling period of the system during the motion-reproduction, this method has to deteriorate the performance of the motion-storing system. In addition, multiple times motion-storing are required to realize several reproduction speed. In this paper, a novel interpolation method based on delta-sigma modulator and the weighted average filter is proposed and evaluated for the implementation of the fractional speed motion-reproduction. The presented interpolation method can achieve the high speed motion-reproduction without degrading the performance of motion-storing system, moreover, it can generate arbitrary reproduction speed from only one-time motion-storing. The effectiveness of the interpolation method is evaluated through several simulations and experiments.