Disclosure is given for a lens grinding apparatus, comprising a pair of lens shafts (5, 5') mounted on a carriage (4), a coarse grinding wheel (1) whith at least two kinds of V-edge grinders (2, 3) and an edge thickness measuring system (10) adapted to measure the edge thickness of the lens (L) held between the lens shafts (5, 5'). The measurements of the edge thickness of the lens (L), the selection of the medium V-edge grinder (2) or the small V-edge grinder (3) and the subjection of the lens (L) to the V-edge treatment can be automatically performed. Therefore, much time and labor can be saved for the operator to lean the machining art and to select one of the suitable grinders or the like.