A method of grinding semiconductor wafers including simultaneously grinding both surfaces of multiple semiconductor wafers by rotating the wafers between a pair of upper and lower rotating surface plates in a state where the wafers are held on a carrier so that centers of the wafers are positioned on a circumference of a single circle, wherein a ratio of an area of a circle passing through the centers of the wafers to an area of one of the wafers is greater than or equal to 1.33 but less than 2.0; surfaces of the fixed abrasive grains comprised in the surface plates are comprised of pellets disposed in a grid-like fashion, with the pellets provided in a center portion and pellets provided in a peripheral portion being larger in size than the pellets provided in an intermediate portion.