A ball bearing in which races are well prevented from flaking in early stages under an environment using lubricating oil having a high traction coefficient so that a long life of the ball bearing is attained, while the cost of the bearing is reduced. The ball bearing has a plurality of balls disposed between a fixed race and a rotating race, and the ball bearing is used under an environment using lubricating oil having a traction coefficient of 0.07 or more under the conditions that a slip factor is 5% and a temperature is 40.degree. C. At least the groove radius of the rotating race is set to be in a range of from 0.53 Dw to 0.58 Dw both inclusive when Dw designates the diameter of balls. In addition, the hardness of the race is set to be in a range of from HRC 58 to HRC 64 both inclusive.