A lens machining apparatus is provided that can execute everything required in machining eyeglass lenses, from measurement to various kinds of machining, and still ensures high-precision machining. The apparatus includes a lens holding unit 12 which holds a lens 1 and causes the same to turn, a cutter 131 which cuts (edges) the circumferential surface of the lens in a prescribed cross-sectional shape, an end mill 141 which machines a groove in the circumferential surface of the lens whose circumferential surface has been cut (edged) and chamfers edges at the lens circumferential surface, and a lens measurement unit 15 which measures the shape and the position of the lens held by the lens holding unit.