Flexible mechanism can transfer or transform the motion, force and energy through the elastic deformation of flexure hinge. This paper propose a novel structural model for U-shaped flexure hinge with large damping based on the damping-free property of flexure hinge and the loss modulus characteristic caused by the shear of viscoelastic damping material. Combined with GHM (Goulla-Hughes-Mactavish) viscoelastic model, a pseudo-rigid-body model with damping hinge is also introduced.The structural damping property of the flexure hinge could be highly strengthened with the help of the shearing effect of viscoelastic damping material. To identify the vibration suppression effect of damping structure for the U-shaped flexure, this paper measured the free vibration signal and conduct the experiments of DMA (dynamic mechanical analysis). The results show that damping loss peak appear in the frequency range of 120~150 Hz through the damping structure design, which effectively enhanced the structural damping property of the flexure hinge.