To predict the viscoelastic responses of fiber-reinforced polymer matrix composites with imperfect interface in the time domain, the effects of viscoelasticity of polymers on the macroscopic/mesoscopic properties of composites are studied on the basis of the micromechanics model. According to the elastic-viscoelastic correspondence principle, a viscoelastic property evaluation method of composites based on the homogenization theory is developed. The boundary value problem and the materials′ homogenization constitutive equation are introduced into the Laplace domain, and then the macro/meso responses of the materials are transformed into the time domain by Zakian′s method with relatively stable performance, thus avoiding the step-by-step iteration of the viscoelastic constitutive with integral form. Different from the classical phenomenological theory and other numerical methods, the present work adopts the Trefftz concept that employs the complete elastic solutions with unknown coefficients to represent the internal trial displacement/stress fields. A spring model with stiffness is introduced to describe the interfacial damage, combined with the functional orthogonality of the analytical expression of fiber/matrix, and the accurate simulation of the interface was realized. Finally, the periodic boundary conditions are applied to the cells by the periodic variational principle, and the macroscopic homogenization constitutive is established to predict the macroscopic properties of materials. The results show that the proposed method can not only realize the efficient prediction of the long-term properties of composites, but also restore the local stress redistribution within unit cells to illustrate the effect of macroscopic modulus degradation.