In the interest of reducing wave loads on offshore structures, this study explores the mitigation of wave loading on a bottom-standing cylinder by surrounding it with a floating annular viscoelastic plate. A matched eigenfunction expansion method is developed within the framework of linear potential flow theory to analyze the hydrodynamic interactions among the incident waves, the central cylinder, and the surrounding viscoelastic plate. The model accounts for both elastic flexural stiffness and viscous damping of the plate, which are tunable engineering properties. Parametric analyses are performed to evaluate the effects of plate rigidity and viscous damping on hydrodynamic responses, including hydrodynamic forces, wave runup, and wave energy dissipation. The results demonstrate that the viscoelastic plate can significantly reduce both linear and second-order wave loads on the central cylinder, provided that its elastic and viscous properties are appropriately engineered. Notably, an optimal range of viscous damping is present that maximizes wave energy dissipation. The study provides useful guidance for the design of floating barriers for offshore structure protection and proposes a tunable, passive wave load mitigation approach.