A retainer for a ball bearing and a ball bearing have reduced torque even in grease lubrication. The retainer includes a retainer body which has an annular shape and has recesses formed in one axial end surface thereof along a peripheral direction at predetermined pitches and a pair of claw portions provided to protrude from opening ends of each of the recesses, the opening ends being opposed to each other in the peripheral direction. Each of the recesses and the pair of claw portions form a pocket in which a ball is received. A pocket has a PCD which is set smaller than a PCD of the ball to be received in the pocket.