A damage-dependent viscoelastic constitutive model for a glass-fiber woven/polyester composite plate is presented in this paper. The constitutive relations were derived within the framework of thermodynamics and continuum damage mechanics from some results of the necessary material tests. The elastic moduli and the damage variable of the material are assumed to be anisotropic. In this theoretical model, both the damage- and the time-dependent properties are phenomenological reflections on the macroscopic deformation process.