This paper introduces a compensating system for machining error, which is resulted from chucking with separated jaws. In machining the chucked cylindrical workpiece, the deterioration of machining accuracy, such as out-of-roundness is inevitable due to the variation of the radial compliance of the chuck workpiece system which is caused by the position of jaws with respect to the direction of the applied force. To compensate the chucking compliance induced error, firstly roundness profile of workpiece due to chucking compliance after machining needs to be predicted. Then using this predicted profile, the compensated tool feed trajectory can be generated. And by synchronizing the cutting tool feed system with workpiece rotation, the chucking compliance induced error can be compensated. To satisfy the condition that the cutting tool feed system must provide high speed and high position accuracy, brushless linear DC motor is used. In this study, firstly through the force-deflection experiment in workpiece chucked lathe, the variation of radial compliance of chuck workpiece system is obtained. Secondly using the mathematical equation and cutting experiment result, the predicted profile of workpiece and its compensation tool trajectory are generated. Thirdly the configuration of compensation system using linear motor is introduced, and to improve the system performance, PID controller is designed. Finally the tracking performance of system is examined by experiment. Through the real cutting experiment, roundness is significantly improved.