In this paper, we have studied about the thermal expansion of the ball screw used for the CNC machine tools. The hollow ball type is used for the ball screw. We have compared the conventional cooling system and function with the improved cooling system and function which is developed the path providing cooling oil in hollow ball screw. That is the temperature variation and positioning accuracy are analyzed of the ball screw. We have obtained the following results through this experiment. 1) The improved cooling system of the hollow ball screw for CNC machine tools was developed 2) The improved cooling system of the hollow ball screw has a large effectiveness on restraining the thermal expansion of the ball screw. 3) The positioning accuracy of the ball screw was improved about 2~4$mu$m using temperature -controlled cooling oil.