More and more isolators are widely used all over the world. For a structure with isolator between base and super-structure, it is suitable to take only the first-mode in consideration for the super-structure, the structure become a 2-DOF system, and its damping and stiffness matrices are non-symmetrical. The equation of motion cannot be decoupled by the mode-superposition method. A complex-mode method is proposed and analytic expressions are obtained under earthquake excitation in the paper. Base on above analytic expressions suggested by authors, an isolator index β(the ratio of the standard deviation of the displacements at the top of super-structure), an optimal design process and some useful data are achieved. All of these are meaningful in practice projects.