The present method of grinding side ridge line portion and a side surface of concrete blocks having the flowing steps: providing a rotating shaft of the grinding machine to be rotationally supported by lower ends of two vertical bars facing each other in the direction in which a conveyor is advanced and suspended from a frame above the conveyor and positioning an axis of the rotating shaft to be laterally and above the conveyor, moving the concrete blocks to a position where it is ground by the conveyor and then positioning the concrete blocks to make side ridge line portions on the bottom surfaces thereof protrude from the conveyor, and grinding the side ridge line portions and/or side surfaces on the upper or the bottom surface of the concrete block by lowering the grinding machine suspended from above the concrete block, the side ridge line portions and/or the side surfaces of the concrete blocks are ground by abutting the grinding machine against the surface of concrete blocks, while at the same time rotating the rotating shaft by a rotating means.