A grinding apparatus that performs thickness measurement across an entire wafer surface without degradation of throughput of wafer grinding and grinds the wafer precisely to a target thickness. A grinding apparatus includes a rough grinding stage for roughly grinding a wafer and a fine grinding stage for finely grinding the wafer. A first thickness measuring means for measuring the thickness of the wafer while the wafer is being transferred is provided to a column so disposed as to span an index table. A control unit of the grinding apparatus corrects a target thickness after fine grinding and computes a target thickness after correction on the basis of an average thickness across the entire surface of the wafer before fine grinding obtained from measured values of the first thickness measuring means.