Viscous-spring artificial boundary is one of the effective means to solve the problem of dynamic soil-structure interaction, but it usually requires a lot of nonlinear dynamic time-history calculation in the process of analysis, and the efficiency is low. This paper aims to establish an efficient calculation method for solving the governing equations of dynamic soil-structure interaction problem with viscoelastic artificial boundary. Therefore, the efficiently inelasticity-separated solve idea is introduced to construct the nonlinear dynamic soil-structure interaction analysis model based on the inelasticity-separated finite element method and viscous-spring artificial boundary. The derived dynamic governing equation is basically same as the governing equation of the fixed boundary that only need to directly add the spring-damper stiffness of the viscous-spring artificial boundary into the initial stiffness matrix and damping matrix of the near-field soil-structure model. In addition, an improved Woodbury approximation method is proposed by combining Woodbury formula with the combined approximation approach, which can reduce the time and space complexity in solving governing equation, and realize the efficient solution of the dynamic governing equation of dynamic soil-structure interaction problem by using viscous-spring artificial boundary. The proposed method retains the advantages of viscous-spring artificial boundary and inelasticity-separated finite element method, and the correctness and efficiency are verified by a numerical example.