An eyeglass lens processing apparatus for processing a peripheral edge of an eyeglass lens, comprising: a lens rotating unit including a lens chuck shaft (102R, 102L) for holding the lens and a motor for rotating the lens chuck shaft; a grindstone rotating unit including a spindle attached to a polishing grindstone and a motor for rotating the spindle; an axis-to-axis distance varying unit including a motor for changing an axis-to-axis distance between the lens chuck shaft and the spindle; a data input unit (5, 7) for inputting target lens shape data; a memory which is adapted to store a rotation speed of the lens and a rotation speed of the polishing grindstone, which satisfy a condition in which an average interval between cyclic stripes appearing on a processed edge surface of the lens which are generated due to height fluctuations of a processing surface of the polishing grindstone with respect to a rotation center of the spindle during one rotation of the polishing grindstone is smaller than 0.06 mm, which is smaller than human eye's resolution, or is larger than 2mm; and a processing control unit adapted to perform polishing by controlling the lens rotating unit, the grindstone rotating unit and the axis-to-axis distance varying unit based on the input target lens shape data so as to polish the peripheral edge of the lens, which has been finished, by a lens margin allowed for polishing by the polishing grindstone, wherein the processing control unit is adapted to control the lens rotating unit and the grindstone rotating unit based on the lens rotating speed and the grindstone rotating speed stored in the memory at least at the final one rotation of the lens. a lens rotating unit including a lens chuck shaft (102R, 102L) for holding the lens and a motor for rotating the lens chuck shaft; a grindstone rotating unit including a spindle attached to a polishing grindstone and a motor for rotating the spindle; an axis-to-axis distance varying unit including a motor for changing an axis-to-axis distance between the lens chuck shaft and the spindle; a data input unit (5, 7) for inputting target lens shape data; a memory which is adapted to store a rotation speed of the lens and a rotation speed of the polishing grindstone, which satisfy a condition in which an average interval between cyclic stripes appearing on a processed edge surface of the lens which are generated due to height fluctuations of a processing surface of the polishing grindstone with respect to a rotation center of the spindle during one rotation of the polishing grindstone is smaller than 0.06 mm, which is smaller than human eye's resolution, or is larger than 2mm; and a processing control unit adapted to perform polishing by controlling the lens rotating unit, the grindstone rotating unit and the axis-to-axis distance varying unit based on the input target lens shape data so as to polish the peripheral edge of the lens, which has been finished, by a lens margin allowed for polishing by the polishing grindstone, wherein the processing control unit is adapted to control the lens rotating unit and the grindstone rotating unit based on the lens rotating speed and the grindstone rotating speed stored in the memory at least at the final one rotation of the lens.