In order to obtain high and stable driving efficiency of ball screw, the design of ball screw pairs with Reuleaux polygon as normal section shape was proposed, and the method of Reuleaux polygon was given. The transmission efficiencies of the ball screw were compared under the same working conditions with Reuleaux triangle, Reuleaux quadrilateral and Reuleaux pentagon as the normal groove shape of the ball screw. The results show that the more the number of Reuleaux polygon grooves is, the higher the efficiency of the ball screw is; taking the Reuleaux pentagon as the normal section of the ball screw is the most reasonable. The transmission efficiencies of Reuleaux pentagon, normal groove ball screw and trapezoidal screw were compared. The results show that the transmission efficiency of the ball screw with the Reuleaux pentagon as the normal section shape is the highest, which is 98.4%, which is 0.8% and 20.6% higher than those of normal ball screw and trapezoidal screw respectively, and the ability of continuous high efficiency transmission is stronger than normal ball screw; theoretically, the smaller the contact angle between the ball and the raceway is, the higher the transmission efficiency of the ball screw is; the size of the equivalent friction angle determines the stability of the high-efficiency transmission of the ball screw; the smaller the equivalent friction angle is, the better the stability of the high-efficiency drive is, and vice versa is weaker.