A ball screw device includes a ball nut having a bore for receiving a screw shaft, and having a number of longitudinal channels and compartments for forming a zigzag shaped fluid flowing passage in the ball nut, a number of deflecting members engaged with the compartments of the ball nut and each having a recess for communicating adjacent channels with each other, the outer peripheral surfaces of the deflecting members are tilted relative to the ball nut for allowing the deflecting members to be expanded when the deflecting members are expanded, a cooling agent flows through the zigzag shaped fluid flowing passage for cooling the ball nut and for preventing the ball nut from being overheated.