To address vibration issues in the operation of a lift-type power catwalk, dynamic analysis was conducted using ADAMS 2020 software. The analysis revealed that the vibrations originate from collisions that occur during the transition from the translation to the climbing phase. A quantitative vibration model was developed using the work–energy theorem, incorporating the coefficient of restitution. Based on this model, a composite disturbance rejection control law was designed, integrating sliding-mode speed planning with active disturbance rejection speed tracking. The MATLAB 2022b/Simulink simulations demonstrated that the ADRC strategy outperforms PID and DDPG control algorithms in terms of robustness. Co-simulation with ADAMS and MATLAB/Simulink confirmed the effectiveness of sliding mode speed planning, resulting in a 13.54% increase in the transport efficiency of lift-type power catwalks for drill pipes. Additionally, the oscillation of the output speed of the electro-hydraulic servo system at the collision point was reduced by 300% and the displacement, velocity, and acceleration fluctuations in the catwalk’s mechanical system were reduced by 85%, 75%, and 90%, respectively. The experiments on a lift-type power catwalk prototype confirmed that the proposed vibration suppression strategy effectively reduces vibrations.