In this paper, seismic elastic and plastic responses of base-isolated structure are investigated, in which the bilinear restore-force model is employed for the isolation equipment. The mutual influences of both damping matrices and stiffness matrices are decoupled by using transition matrix. Based on the increment-dimensional precise integration method (PIM), the increment -dimensional blocks PIM is developed to separate structure characteristics and external forces, which can avoid the calculation of exponential matrices by PIM in each integration step. The results of numerical examples show that the efficiency of the new algorithm is very high in comparing with old method. The advantages of the new algorithm appear more obvious when the characteristics of large-scale structure have slightly changed, and only the external forces vary.