Sloshing in partially filled containers is a key phenomenon for the design of offshore structures such as liquefied natural gas carriers, floating production storage and offloading platforms, crude oil carriers, and floating liquefied natural gas vessels, due to large sloshing force acting on container's walls. Hence, violent sloshing motion needs to be mitigated for the safe operation of the floating structures. This study is focused on the experimental investigation of a sloshing damping device based on floating balls. The free-surface sloshing waves are generated in a rectangular tank filled with water, the free-surface of which is covered by a layer of floating balls. Three important sloshing regimes, namely, shallow, intermediate, and finite-water depth sloshing, are considered for investigation. Frequency responses of sloshing with and without balls are obtained to comprehend the effects of floating balls on damping of sloshing odd modes (first, third, fifth, and ninth modes). Further, physical processes enhancing damping mechanisms are also investigated in detail. It is found that the floating balls dampen shallow-water sloshing effectively. Different motions of the balls, ball–ball interactions, motions of ball–liquid interfaces, and liquid shear-flow motion between the tank wall and balls cause the dominant mechanism of energy dissipation.