Under high-speed and heavy-load operating conditions, the vibration of wire rope inevitably occurs due to the error of the wire rope itself and external interference, which greatly affect the service life of the wire rope and the comfort of passengers. In this paper, a friction hoist is taken as the research object, Hamilton principle is used to establish the dynamic model of the system, and adaptive robust theory is used to design the boundary control strategy of the longitudinal vibration suppression of the hoisting wire rope, and Lyapunov theory is used to prove the stability of designed controller. The simulation results show that the designed adaptive robust controller can effectively compensate the vibration displacement shift caused by the elastic deformation of the wire rope, and obtain a faster convergence rate of vibration suppression than traditional proportion integration differentiation (PID) algorithm.