According to the philosophy of “partially weaken the core element of the BRB to protect the other part”, 12 specimens of the Triple Square Steel Tube Buckling-Restrained Brace (TSST-BRB) were designed with which the core element had notched. ABAQUS finite element method was used to investigate the performance of TSST-BRB with different notched kinds, number, length and depth of the core element. The analysis results indicated that the core element with annular notch was conducive to reduce the stress concentration of ends, and dissipate energy under tiny displacement. Two notches of the core element were better to reduce the peak stress of the notched segment and the stress concentration of ends. The length of notch should be controlled on 13.3%~20.0% of the length of core element. The energy dissipation capacity, yield displacement and yield capacity of the TSST-BRB were significantly influenced by the depth of notched core element. The depth of the notch should be controlled on 10%~23.3% of the thickness of core element.