An apparatus for grinding a substrate includes a stage part configured to support a substrate thereon, a grinding part, a camera part, a replacing part and a control unit. The grinding part includes a grinding wheel configured to grind an edge of the substrate. The camera part is configured to take a picture of the grinding wheel, analyze the picture of the grinding wheel and generate information about the grinding wheel. The replacing part includes a spare grinding wheel and is configured provide the spare grinding wheel to the grinding part or pick up the grinding wheel from the grinding part. The control unit is configured to receive the grinding wheel information from the camera part and offset compensate a position of the grinding wheel on the basis of the grinding wheel information or communicate with the replacing part to replace the grinding wheel on the basis of the grinding wheel information.