Abstract: The vertical vibration of the rolling mill is a key issue in the low production efficiency of cold-rolled strip products, which seriously affects the quality of rolled products and the improvement of rolling speed. In order to improve the safety of rolling mill equipment, production efficiency and steel accuracy, this paper studies the vibration characteristics and vibration reduction effect of rolling mill roll systems based on active and passive damping shock absorbers. Firstly, a fractional order time delayed vertical nonlinear vibration equation with active and passive damping shock absorbers is established through considering some factors of the fractional order and time delay in the active damping control effect; Then, the analysis of stability is conducted on the established mathematical model, and the stable regions of various parameters of the active and passive damping shock absorbers are obtained; Furthermore, the multi-scale method is used to obtain the amplitude frequency equation of the system, and the time-domain characteristics, spectral characteristics, main resonance characteristics, and subharmonic resonance characteristics of the system are analyzed; Afterwards, a time-delay feedback control is applied to the vibration response of the rolling mill roll system, and the amplitude, irregular vibration, and energy consumption of the vibration system are optimized by achieving the optimal feedback control gain and optimal feedback delay; Finally, the vertical vibration control experiments are conducted on the working rolls of the stationary rolling mill, and it is found that the theoretical analysis is in agreement with the experimental results principally. The results show that the active and passive damping shock absorbers can effectively suppress the vertical vibration of the rolling mill roll system and meet the requirements of design. The results provide reference for the design and application of the shock absorber of rolling mill roll system and the vibration control of rolling mill.