In this research,the vibration of elevator ropes,including the main rope and compensation rope are investigated simultaneously in a high-rise elevator system under earthquake excitation.Moreover,the paper presents a new control method to restrain the sway of both ropes.This study considers varying rope lengths during elevator operation which cause other system parameters such as natural frequency,and damping ratio to be time-variant variables.The dynamics of the ropes are analyzed by solving the goving non-stationary,nonlinear equation numerically.In order to mitigate the vibration of ropes in several motion conditions,particularly upwards movement,downward movement,stopped at the lowest position,and stopped at the highest position,an active equipment is installed at the compensation sheave.The stability of the system using the controller is analyzed at four states:without disturbance and static car,without disturbance and mobile car,including disturbance and static car,and including disturbance and mobile car.The efficiency of the controller used for dampening the vibration of elevator ropes is validated by numerical simulation results.