Abstract: To address the risk of the excessive displacement demand of the isolation layer in the friction pendulum bearing (FPB) based an isolation system subjected to severe earthquake excitation, a hybrid isolation system with the tuned inertia electromagnetic damper and FPB (TIED-FPB) is proposed. Considering the mechanical nonlinearity in FPB and electromagnetic damping, the governing equation of the TIED-FPB system is constructed by simplifying the base-isolated structure into a two-degree-of-freedom (two-DOFs) system. By virtue of the stochastic equivalent linearization model of FPB and electromagnetic damping, the equivalent tuned inerter damper (TID)-two-DOFs system is constructed. The closed formula for the design frequency ratio and damping ratio of the equivalent TID is derived by considering the H₂-norm of the basement displacement response under the white noise excitation. In the combination with the complex mode analysis, complex complete quadratic combination (CCQC), and stochastic vibration analysis, the maximum responses of the basement displacement and the relative velocity of linear viscous damping in TID are approximated when the isolation system subjected to the power spectrum density excitation. Given the displacement demand target of the isolation layer, the mass ratio of the TID is obtained through the iterative update strategy. The critical velocity and critical damping coefficient of electromagnetic damping in TIED are determined from the maximum relative velocity and the equivalent damping ratio of the damping in TID, further realizing the demand-oriented design of the TIED. To verify the feasibility of the optimization method proposed and the seismic performance of the TIED-FPB isolation system, a new uniaxial material for mimicking the electromagnetic damping was added in OpenSees software, and 44 seismic ground motions were selected according to the standard design spectrum to perform the nonlinear time history analysis of a 7-storey seismic isolation benchmark model. The time history results illustrate that the TIED-FPB system is superior to the FPB-based BI system in terms of the mitigation of the isolator deformation and the robustness of the acceleration response.