In this paper, a vibration isolator using a viscoelastic material is proposed for reducing the micro- vibration in satellite platforms. In order to describe the vibration isolator, a mathematical model is derived in six degrees of freedom: three translational and three rotational motions. Then, the mathematical expressions of the force and moment transmissibility, which can evaluate the amount of reduction in micro-vibration through the vibration isolator, are established. The proposed mathematical model for vibration isolator is verified by comparing the transmissibility plots obtained from the mathematical model and the ANSYS results. Finally, the effect of the design parameters on the isolation performance is investigated using the mathematical model.