Typical engineering cable structures, such as high-voltage wire and wire rope, usually bring a damping effect which cannot be ignored due to the technological problems of manufacturing. For such problems, especially the damping of cable structures undergoing large displacement and severe deformation, few studies have been reported in the past. In this work, the fractional derivative viscosity model is introduced into the cables described by the absolute nodal coordinate formulation. The computer implementation algorithm of the proposed cable damping model is given based on the three-parameter fractional derivative model. Two numerical examples demonstrate the effectiveness and convergence property of the proposed cable damping model. An experiment is proposed in which a wire is tensioned and released. Configurations are captured by the high-speed camera and compared with the results obtained from the numerical simulation. The agreement of the simulation and experimental results validates the proposed cable damping in application.