Based on a new variational principle in the time domain, a substructure synthesis method is developed for non-symmetric viscoelastic systems without precluding a symmetric formulation. The viscoelastic damping is assumed to be generally non-proportional and in an hereditary integral form. The traditional state space formulation is avoided by the proposed substructure synthesis method so that the approach is independent of viscoelastic models. On the basis of the Rayleigh-Ritz approach, each substructure is approximated by a set of admissible trial vectors. In accordance with substructure order reduction, the geometric compatibility conditions can be approximated by a weighted residual method. The method is independent of the viscoelastic damping models and the effort on the reduction process is similar to that of classic methods for undamped systems. If all the coefficient matrices are symmetric, the formulation preserves the symmetry in the reduced systems by choosing the same trial vectors and weighting vectors for both the original and adjoint systems. In the absence of damping, the method is further reduced to classical component mode synthesis if undamped substructure modes are used as trial vectors.