Based on the micromechanical theory of Eshelby-Mori-Tanaka and Weibull's theory of statistics,the viscoelastic constitutive relationship of composite solid propellant with interfacial damage was established in this paper.The influence of interfacial damage for 3 kinds of uniform,circumferential and top spilt on the viscoelastic constitutive relationship of the propellant was studied.Numerical analysis showed that the influence of interfacial damage on the viscoelastic constitutive relationship of the propellant was obvious,and made it exhibit highly nonlinear viscoelasticity.The extent of different interfacial damage model affecting the constitutive relationship of the propellant was different.