As a composite material, the damping energy consumption mechanism of fiber reinforced polymer-confined reinforced concrete (FRP-C RC) structure is very complex. In previous dynamic calculation models, the bond-slip effect for steel bars was often ignored, which would lead to a considerable error in the response of the FRP-C RC structures. In this paper, a new numerical model of FRP-C RC columns considering the bond-slip for steel bars is established using a zero-length element and nonlinear beam-column elements in the OpenSees software, and the results of the model are verified by experimental results. Based on the complex damping theory, the loss factor expression and nonlinear damping model of FRP-C RC columns with the bond slip effect are proposed. Finally, the dynamic response of FRP-C RC columns with nonlinear damping under harmonic load is calculated and compared with the results available in literature. The results show that the proposed model considering steel bars’ bond-slip can provide better prediction for dynamic response of FRP-C RC columns and make the future seismic design of FRP-C RC columns safer.