Abstract: In this paper, a method for improvement of the roundness by making compensation for the spindle rotation error motion（SREM） is presented.The compensatory system based on the characteristics of SREM is composed of capacitance sensors, A/D D/A converter, IBM-PC/XT computer and piezo -electric actuator. Time series analysis theory and simulation of SREM show that stochastic compensation can improve the roundness up to 85%. The transfer function of the over ail System is derived, and method of optimal parameter selection is developed.Experimental results show that the roundness error of workpiece can be reduced to less than 0.05μm. A improvement of more than 60% while the surface roughness of workpiece（ 12） is not affected.