Offshore platforms are located in the harsh environment. Environmental loadings such as wind and sea wave may result in excessive vibrations to these offshore structures. Inerter-based element can generate an apparent mass that is much larger than its physical mass, it also can generate a negative stiffness to the system. It therefore has the potential to be applied to mitigate the adverse vibrations of offshore SSPs. This presentation introduces some recent developments in this area. In particular, analytical studies that utilise the mass amplification effect and negative stiffness effect of the device will be introduced first, the experimental studies on a newly developed inerter damper and large-scale water flume tests on a SSP will also be introduced