The gear backlash is in the process of gear and rack transmission,the gear backlash needed to be eliminated to ensure the bidirectional transmission precision of the transmission mechanism. In the designed mechanical mechanism,two racks meshing gears is driven through the axial relative displacement of the mechanism of sliding lead screw nut,and an axial relative displacement between the two racks（ gear rack staggered teeth） appeared,and the equivalent tooth thickness increased,and one mechanism is designed to eliminate gears backlash automatically. The mechanism is used in rotary table of NC machine driving by gear- rack successfully,it can obtain simple structure and high transmission precision.