Viscoelastic material have been extensively used in engineering applications to reduce structural vibration.But, the viscoelastic materials are often required to exhibit different properties in different places of structure, when its in specified operating situations.The purpose of this papar is to investigate the design approach of microstructures of viscoelastic composites with specific properties.The composite is considered to have a periodic microstructure, which is composed of elastic inclusions and viscoelastic matrix.The optimization problem is formulated as designing the arrangement, shape and size, and volume fraction of the elastic inclusions or pores in the viscoelastic material matrix to achieve the specific effective viscoelastic properties of composite material.The effective behavior of composite materials is predicted by use of a finite element based homogenization procedure.The objective function is to minimize the square of the differences between the components of effective viscoelastic moduli and the desired (given) values.The optimization problem is solved using the programming method.Several examples of optimal design of composite material are presented to demonstrate the validity of the present design approach.