A cable-braking apparatus includes a main body unit at which a main cable is positioned, a drive unit provided at the main body unit so as to generate a drive force, an elastic compression unit configured to compress or release the main elastic element using the drive force generated by the drive unit, a press unit actuated by the elastic compression unit so as to move a press plate thereof to thus press the main cable, and a movement control unit configured to lock or release an anchor pin to thus control movement of the press unit. The main elastic elements are compressed and released by the action of the gear train and the clutch, thereby offering an effect of preventing malfunctions.