Abstract: To address the risk of the excessive displacement demand of the isolation layer in the friction pendulum bearing (FPB) based isolation system subjected to severe earthquake excitation, a hybrid isolation system with tuned inerter electromagnetic damper and FPB (TIED-FPB) is proposed in this paper. 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 TID-two-DOFs system is constructed. The closed formula of 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 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 viscous damping in TID were 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 proposed optimization method 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-story seismic isolation benchmark model. The time history results show that compared with the FPB-based BI system, the proposed TIED-FPB reduces the displacement response of isolation by 25.8% and improves the robustness of acceleration response by 32.3%.