A practical analysis method for inertia damper energy dissipation systems composed of building structures with inertia dampers is proposed，including of concise closed-form solutions for the random seismic response and a practical setting strategy for inertia dampers. Based on the mechanical structure diagram of the series inertial damper and installation method in buildings，the coupled seismic motion equation of the energy dissipation system is established. In response to the difficulty in solving the damping and stiffness parameters in the actual dynamic equations of structures，an equivalent form of the uncontrolled structure represented by real modal vibration parameters is obtained based on finite element technology and dynamic principles，and the dynamic equation of the inertia damper energy dissipation system is reconstructed. Based on the quadratic decomposition method of the power spectral density function，closed-form solutions of the spectral moments of the building structure relative to ground displacement，interlayer displacement，and inertial damping force are derived. The correctness of the proposed concise closed form solution is verified through numerical examples，and the influence of real mode number on the 0~2 spectral moment of series response and the influence of floor position of inertia dampers on the seismic reduction effect of structures are studied. Results show that，using the number of actual vibration modes corresponding to the cumulative participation coefficient of 100% in the free vibration analysis of uncontrolled structures can achieve stable analysis accuracy and computational efficiency for the response analysis of multi-degree of-freedom energy dissipating structures，and to use reducing interlayer displacement of uncontrolled structures as the placement strategy for installation of inertial dampers is simple and feasible. This paper can provide a reference for the analysis of random ground motion response of complex building structure with series inertia capacity system.