The present invention relates to an elevator wire rope braking apparatus, and more particularly, to a rope braking apparatus which prevents partial abrasion of the wire rope while increasing braking efficiency by preventing a deviation in the pressure applied to the wire rope by a pressure plate moving in a straight line to apply pressure to the wire rope. Since the pressure application is based not on a hydraulic method but on a purely mechanical structure using only a spring elastic force, environmental pollution caused by hydraulic oil may be prevented and product cost may be reduced.