•A TYRSFB was proposed to esnhance the post-yielding stiffness of the RSFB.•The theoretical top force–displacement curves of RSFB and TYRSFB were derived.•Quasi-static tests and numerical simulations were conducted on the TYRSFB.•Influences of steel rod configuration on the performance of the TYRSFB were studied. The lower post-yielding stiffness of a buckling-restrained brace (BRB) was improved by constructing a two-level yielding BRB by setting an additional unit with a certain stiffness after the yielding of a traditional BRB. In this paper, a pinned steel rod with an initial gap is added at the outside of each buckling-restrained column (BRC) in a rocking steel frame with BRCs (RSFB) to improve the stiffness, lateral carrying capacity and ductility of the RSFB after BRCs yielding, which is named as a two-level yielding RSFB (TYRSFB). This paper studies the seismic performance of the TYRSFB and determines the influence of key constructional parameters of steel rods on structural performance. First, the top force–displacement curves of the TYRSFB are derived. Then, quasi-static tests and numerical simulations are conducted on the TYRSFB and RSFB, and the results show that the proposed TYRSFB can achieve the anticipated seismic performance. Moreover, the numerical simulation results are basically consistent with the calculation results of the proposed theoretical formulas. Finally, parametric studies based on the theoretical formulas and numerical models show that changing the value of the distance between steel rods and the central column, the initial gap, the ratio of the cross-sectional area and the length between the steel rod elastic and energy dissipating portions will influence the structural lateral carrying capacity, ductility and failure mode.