A rotation support device for a compressor pulley, wherein a three-point contact radial ball bearing (14b) is used as a rolling bearing for supporting a driven pulley, the cross sectional shape of an inner ring raceway track (19b) coming into contact, at one point, with the rolling contact surface of each ball (17a) is formed in a composite arc by smoothly and continuously connecting arcs with different radii of curvature R.sub.1 and R.sub.2 to each other, and the radius of curvature R.sub.1 on a center side in the width direction is made smaller and the radii of curvature R.sub.2 on the both end sides in the width direction are made larger (R.sub.1