Annular tuned liquid dampers (TLDs) may be installed in slender structures with limited floor space, in which people and utilities must pass through the core, such as a wind turbine or observation tower. This study investigates an annular-shaped TLD equipped with damping screens. A linearized equivalent mechanical model capable of capturing the fundamental sloshing mode response of an annular TLD is presented. An experimental shake table testing program is completed to assess the performance of the model. Thirty-six frequency sweep tests consisting of various TLD configurations, excitation amplitudes, and excitation directions are completed. Good agreement is observed between the linearized equivalent mechanical model and experimental wave heights, sloshing forces, and energy dissipated per cycle that have been filtered to include only the fundamental sloshing mode response. The model is also observed to be in good agreement with experimental data for different excitation directions. The model is coupled to a generalized structure to investigate the response of a structure equipped with an annular TLD. The annular TLD is found to reduce the response of a generalized offshore wind turbine structure undergoing harmonic force excitation. The annular TLD provides performance comparable to an optimal linear tuned mass damper (TMD) with the same properties for a range of force excitation amplitudes.