Abstract: According to the relationship between viscosity coefficient of viscoelastic damping model and loss tangent of complex damping model,and the consistency of structural vibration response,the general expression of viscosity coefficient and loss tangent of viscoelatic material was deduced by SDOF's dynamic analysis when the system was in steady-state harmonic vibration or free vibration.Furthermore,the experimental investigation was carried out to study the frequency-dependent viscosity coefficient and loss tangent of fiber reinforced concrete material.It has been shown that,for the steady-state harmonic vibration and free vibration,the expressions of viscosity coefficient and loss tangent were identical except the given vales of frequency.The loss tangent and viscoelastic coefficient of fiber reinforced concrete was decreased with increasing frequency,and decreased shapely among 0.5 to 1.0Hz,then decreased smoothly.Compared with the control plain concrete,the influence of frequency on loss tangent and viscoelastic coefficient of fiber reinforced concrete was more significant.The frequency-dependent viscosity coefficient and loss tangent and the deduced two parameters expression,validated by experiments,are significant important for building damping coefficient or damping matrix which have explicit physical meaning and is convenient for structural vibration response analysis.