This paper presents microstructural topology optimization of viscoelastic materials for damped structures. The microstructure is composed of periodic unit cells. The effective modulus of the viscoelastic material is obtained through the homogenization method. The density-based topology optimization is adopted to find optimal microstructures of viscoelastic materials. The design objective is to effectively attenuate transient responses of damped structures. Transient responses are evaluated with an implicit time integration scheme based on the two-scale analysis. An adjoint sensitivity analysis is developed for computation of the derivatives of transient responses of macrostructures with respect to microstructural design variables. Several numerical examples demonstrate the effectiveness of the proposed approach. Various microstructures of viscoelastic materials are presented, and their corresponding transient responses of the damped structures are discussed. (C) 2018 Elsevier Ltd. All rights reserved.