Damping plays an important role in suppressing modal vibration in a flexure-based mechanism due to its lightly damping characteristics. This paper develops a novel damped circular hinge with integrated comb-like substructures, and derives a mathematical model of loss factor of the flexure hinge and builds its pseudo-rigid body model with damping. The damped flexure hinges can be fabricated in a hybrid process with additive material manufacturing or mounting, and damping-material filling by means of some designed aided tools. For the actual fabricated damped circular hinges, their modal loss factors in a specified sandwiched-damping-layer configuration are obtained based on experimental modal analysis, as indicate that sandwiched damping can effectively suppress the bending modal vibration and the damping can be reinforced progressively with a damping-layer number. Meanwhile, based on finite element analysis, loss factor of the damped flexure hinge and its mathematical model are verified. The actual and simulation experimental results indicate that the presented comb-like damped substructures can be effectively functioned as a modular damper for a circular hinge and the damped flexure hinge can be designed independently of its damping and stiffness when low elastic viscoelastic material adopted.