Abstract: A three-dimensional fluid-structure interaction (FSI) model with arbitrary Lagrangian-Eulerian(ALE) liquid-structure coupling and sliding-mesh fluid-fluid coupling of a displacement-sensitive (DS) liquid damper with cylinder-wall grooves was constructed. The synchronous-iterative FSI method combined with the moving mesh control method was utilized to calculate the dynamic responses of the damper system under dynamic excitations. The results were partially verified by experiments. Several important problems were analyzed, including the damping characteristics under a high-speed and shock input, effects of the piston’s initial position offset and the grooves’ structural variation on the damping characteristics. The results show that the offset of the piston’s initial position along the direction of the compression stroke was favorable, but the initial piston offset along the direction of the extension stroke was unfavorable. The damper with cylinder-wall grooves could reduce the instantaneous peak of damping force under a shock condition. The damping characteristics of the damper with multi-grooves showed to be an approximate superposition of the effect of each groove. The damping ratio was increased when the piston velocity amplitude decreased. The damping force fluctuation occurred when the groove paths were opened and closed under higher speed conditions, but it could be improved by extending the end section. These results are helpful for the design of the passive controlled damping characteristics of this kind of liquid dampers.