To provide a cup type superabrasive wheel and a method of surface grinding for a wafer, by which highly precise grinding operation can be performed without generating a recessed portion at the rotation center of a workpiece, such as a wafer.

Tips 1, 2 having two different active face areas are fixed on the end face of the cup type base metal, the end face being perpendicular to the axis of the cup type base metal. The distance R1 from the axis of the cup type base metal to the farmost end portion of the tip 1 having the large active face area is set so as to be longer than that of the tip 2 having the small active face area. The width T2 of the tip 2 having the small active face area is set so as to be smaller than that T1 of the tip 1 having the large active face area. A circle or an ellipse is favorable to the shape of the tips. Further, setting-up is carried out such that the rotational center of the wafer is ground only by the tip having the large active face area.