The additional tuning mass damper is a traditional control technique for the chimney， but it usually requires a large addi? tional tuning mass and auxiliary installation space， which brings inconvenience to the construction and installation. This study pro? poses utilizing the additional tuned mass inerter system （TMIS） to reduce seismic responses of the chimney. The apparent mass ef? fect of the inerter is employed to achieve the goal of lightweight control. Meanwhile， considering that the influence of high-order modes of the high-rise chimney on its seismic responses cannot be ignored， the distributed TMISs arranged along the height of the chimney are proposed to achieve the multimode control effect. Mechanical models of the TMISs based on two different inerter sub? systems are established， and the equations of motion for the chimney with corresponding additional distributed TMISs are estab? lished. Taking Kanai-Tajimi’s spectrum as the random seismic excitation input and based on the extended fixed-point theory， the simplified assumptions for part of the design parameters of distributed TMISs are proposed. The demand-oriented multimode opti? mization design method for the chimney with distributed TMISs is presented. The effectiveness of the proposed design method is verified by a design case. The lightweight and multimode control effects of additional distributed TMISs are examined by compara? tive analyses. The rationality of the simplification based on the extended fixed-point theory is verified through parameter analysis. The results show that the proposed design method can achieve the expected target performance using the two distributed TMISs. Both the two distributed TMISs behave obvious lightweight control effect.