Damping as a material property plays an important role in decreasing dynamic response of structures. However, very little is known about the evaluation and application of the actual damping of Fiber Reinforced Polymer Confined Reinforced Concrete (FRP-C RC) material which is widely adopted in civil engineering at present. This paper first proposes a stress-dependent damping model for FRP-C RC material using a validated Finite Element Model (FEM), then based on this damping-stress relation, an iterative scheme is developed for the computations of the non-linear damping and dynamic response of FRP-C RC columns at any given harmonic exciting frequency. Numerical results show that at resonance, a considerable increase of the loss factor of the FRP-C RC columns effectively reduces the dynamic response of the columns, and the columns with lower concrete strength, FRP volume ratio and axial compression ratio or higher longitudinal reinforcement ratio have stronger damping values, and can relatively reduce the resonant response.