A position control method for interpolating aspherical grinding and polishing tool path was reviewed and experimented in a nano precision machine. The position-base algorithm was reformed from the time-base algorithm, proposed in the previous study. The characteristics of the algorithm were in the velocity control loop with position feedback. The aspherical surface was divided by an interval at which each velocity and acceleration were calculated. The theoretical velocity was corrected by position error during processing. In the experiment, a machine was constructed and nano-scale linear encoders were installed at each axis. Relation between process parameters and the variation of position error was monitored and discussed. The best result from optimized parameters showed that the accuracy was 150nm and improved from the previous report.