Under most cases, the non-liner energy dissipation is approximately replaced with Rayleigh damping model which belongs to Maxwell-Kelvin type, the method is a fuzzy evaluation method of damping. Based on complex damping theory, equivalent dynamics equation of complex damping model is derived and loss factor is discussed, the accuracy of the equation is theoretically confirmed in this paper. Based on the existing damping theories, a new damping model is proposed, which is a zero amplitude damping model combing with stress dependent complex damping model. The model is used in seismic resistance analysis. Taking a steel beam for an example, the relationship between response amplitude and damping ratio is analyzed with the new damping model. It shows that the method of stress-dependent damping with consideration of zero amplitude damping can precisely describe the energy input and energy dissipation principles and the dynamic response under seismic loads can be precisely obtained. A solid foundation is laid for the further study of complex damping theory, its equivalent viscous damping model and engineering application.