Abstract: Because of the low stiffness of the ball screw with a large aspect ratio, the dynamic characteristics of the ball screw have significant time-varying characteristics with the change of the grinding position during the grinding process. Therefore, it is difficult to ensure the stability of the ball screw during the grinding process, affecting the surface quality and wear resistance of the ball screw, and reducing the grinding efficiency and accuracy retention of the ball screw. In this paper, the stability analysis method of doubly regenerative for the ball screw time-varying grinding system was proposed to predict grinding chatter more accurately and improve the grinding surface quality and machining efficiency of the ball screw. The modal formation function of the transverse vibration of the ball screw was established based on the Euler-Bernoulli beam theory, the continuity condition, and the boundary condition of the elastic beam. The grinding dynamic model of the ball screw with fixed supports of multiple steady rests was established, and the time-varying dynamic characteristics of the ball screw at different grinding positions during the entire grinding process were analyzed. The grinding chatter mechanism of the doubly regenerative of the ball screw grinding system was expounded, and the grinding stability in the whole grinding process and at the weakest position of dynamic stiffness of the ball screw was analyzed. The NSGA-Ⅱ genetic optimization algorithm was used further to optimize the support position of the steady rests. The stability analysis of doubly regenerative for the ball screw time-varying grinding system and the optimization of the support position of the steady rests provide a basis for reasonable selection of grinding parameters and ensure the stability of the ball screw in the whole grinding process.