Fluid-structure interactions, especially full rotor simulations for wind turbines, are still computationally inefficient. Although the Proper Orthogonal Decomposition (POD) -Galerkin based Reduced Order Modelling (ROM) has become a popular tool to solve many fluid dynamics problems, most studies are limited to fluid flows in a fixed or infinite domain. The ROM, with either spatially or temporally adaptive snapshots, are still lacking in research, and in this paper, a POD-Galerkin based ROM for a FSI problem is proposed. The aim is to reduce the complexity of the costly solution techniques for solving the governing non-linear unsteady partial differential equations that govern the aerodynamic flows over fluid-solid systems with moving interfaces. This novel POD-based ROM is applied to several cases of plunging-pitching aerofoils as well as fluid-structure interaction simulations of a 3D vertical axis wind turbine full rotor simulation. For both applications, this model is shown to be very effective when performed with the proposed snapshot grids, thus reducing the computational cost while maintaining the same level of accuracy.