In this paper, a methodology of geometrical error identification and compensation for NC machine tool position is developed. We propose a reference artifact with measuring the geometry of coordinate system for compensating linear scale error of NC machine. The coordinate system of the NC machine could be compensated successfully with the information obtained by measuring the reference artifact and our compensation algorithm. Monte Carlo simulation is used to evaluate coordinate referencing ability and, the uncertainties of the machine tool position is estimated and observed through the compensation process by simulation.