By neglecting the viscosity of fluid and rotation in flow, the theory of potential flow cannot accurately predict the hydrodynamic forces on the structures under significant viscous effects. In this study, the effects of liquid viscosity on the hydrodynamic forces on a horizontal circular cylinder underwater with a large-amplitude forced oscillation were investigated. The study used a two-dimensional two-phase flow wave tank model based on the viscous fluid theory using the OpenFOAM® package. The numerical calculations were carried out under different types of liquid (i.e., liquid with different viscosities). The liquid viscosity effects are visually shown by comparison of the various frequency components of the hydrodynamic forces on the cylinder, and the magnitude and phase relations of the viscous shear forces and the pressure forces. By analyzing the distribution characteristics of the flow fields around the circular cylinder, the viscous-effect mechanisms are revealed. It is found that the discrepancies of the contributions of viscous shear forces, and the discrepancies of the vortex effects on the phase and magnitude of the pressure forces lead to the obvious differences among the results under different liquid viscosities.