An eyeglass lens processing apparatus includes: a processing tool which processes a peripheral edge of the lens and includes a roughing tool, a beveling tool and a bevel-modifying tool; a selection unit which is used to select a high curve beveling mode for forming a bevel in the lens fitted into a high curve frame having a protrusion portion; a modifying portion data input unit inputs data of a portion to be modified so as to prevent an interference between the lens and the protrusion portion; a calculation unit which obtains bevel-modifying data on the basis of a bevel path and data of the modifying portion; and a processing control portion which performs the beveling to the lens by the beveling tool in accordance with the beveling data, and removes a part of the bevel shoulder and/or the bevel slope by the bevel-modifying tool in accordance with the bevel-modifying data.