Diagrid tube structures have advantages on constructing high-rise buildings for its great lateral stiffness, but its seismic design methodology researches are limited. The two-stage design method in Chinese code is not specific enough for the seismic fortification objectives of this kind of structures. It is necessary to propose some specific seismic performance objectives for the key components. Typical CFST diagrid tube-concrete core tube structures are studied by dynamic elastic-plastic time-history analysis using Perform-3D program. The structure plasticity developing process is summarized and the distribution characteristics of seismic fortification lines between tubes are discussed. The influences of main structure lateral stiffness related factors on the plasticity developing process are researched. The key components of structure lateral stiffness and plastic energy dissipation are studied. The seismic performance objectives of the key components are proposed for the three-level seismic fortification objectives.