A topology optimization for the design of rubber vibration isolators is proposed. Many vibration isolators are made of rubbers and they operate under small oscillatory load superimposed on large static deformation. Vibration isolators must have a certain degree of static stiffness in order to endure the static loading due to large gravitational and inertial forces. On the other hand, isolators must have a small dynamic stiffness in order to reduce the force transmission from vibrating systems to base structures. Therefore both the static and dynamic behaviours of rubber should be simultaneously considered in the design process. The static behaviours of rubber under large and slow loads are generally treated with hyperelastic constitutive models. Rubber under fast dynamic loads can be modelled as a viscoelastic material. In this paper, the steady state viscoelastic model, which is suggested by Kim and Youn and correctly predicts the influence of the pre-strain on the relaxation function, is applied for the dynamic analysis. The continuum-based design sensitivity analyses (DSA) of both the static hyperelastic model and dynamic viscoelastic model are developed. The topology optimization formulation is proposed in order to generate the system layouts considering both the static and dynamic performance. The density distribution approach and sequentially linear programming (SLP) are used as the optimization algorithms. Some design examples are presented in order to verify the proposed approach.