A vehicle wheel bearing apparatus has a double row angular ball bearing including double rows of ball groups. A pitch circle diameter of the double row ball group of the outer side is larger than a pitch circle diameter of the double row ball group of the inner side. The outer member is made of medium carbon steel including carbon of 0.40.about.0.80% by weight. It is hardened by high frequency induction quenching so that each of the outer raceway surfaces is formed with a hardened layer having a surface hardness of 58.about.64 HRC. The effective depth of hardened layer is set at at least 2 mm. The minimum wall thickness of the outer member at these outer raceway surfaces is set at at least 4 mm.