We studied the effective behavior of a composite made of a periodic distribution of inclusions linked to a matrix by a very thin layer, with the three components being of linear Kelvin-Voigt viscoelastic type. The effective behavior, derived by a rigorous mathematical homogenization method, is not of Kelvin-Voigt type but instead involves an additional fading memory term. The influence of various parameters of the composite were numerically analyzed through a finite elements method.