A lens grinding apparatus is improved to ensure that the angular edge portions of an eyeglass lens are easily ground to a desired shape. The improved lens grinding apparatus comprises input means for entering data on the shape of a lens to be processed, means for detecting the edge position of the subject lens on the basis of the entered shape data, first calculating means for determining processing data on the rough and fine processings of the subject lens on the basis of the detected edge position and the entered shape data, angular edge portion processing means which has a grinding wheel to process the angular edge portions of the finely processed lens and which moves the shaft of said grinding wheel relative to a shaft holding the subject lens, second calculating means which sets a plurality of zones of the subject lens and which performs different calculations in different zones such that the amount of processing the angular edge portions is determined in correspondence with the radius vector angle of the subject lens, and means for controlling the processing of the subject lens on the basis of the results of calculation by said first and second calculating means.