To provide a ball screw support structure both economical and compact without impairing reliability and durability.

An engaging part 2 and a shoulder part 9 for positioning are formed in the outer periphery of the screw shaft 1, a predetermined quench-hardened layer is formed through the high frequency hardening on the surface of the engaging part 2 and the shoulder part 9, while the end portion 2a of the engaging part 2 is left as an unbaked part having a raw material surface hardness, the inner race 6 of a rolling bearing 3 is pressed into the engaging part 2 through a predetermined interference and in a state that the inner race 6 is abutted to the shoulder part 9, the end portion 2a of the engaging part 2 is deformed outward plastically in the diameter direction, and a caulking portion 11 is formed in 3 points equally placed in the periphery in a coherent state over a chamfer 6a from the end surface 6a of the inner race 6 and by this caulking portion 11, and the inner race 6 is fixed in the axial direction against the screw shaft 1. By this way, manufacturing manpower and the number of parts are kept to the minimum, leading to simplified assembly works and also to low cost, and the support structure is downsized.