The seismic performance of an H-shaped core buckling-restrained brace (HBRB) is evaluated through detailed finite element analysis. The numerical model is validated against available experimental data and a parametric study is carried out to investigate the effect of influential parameters on the cyclic behavior and failure modes of HBRB. Several design parameters including the yielding length ratio, the constrained length, the presence of stiffeners and their thicknesses, the length of the transition region, and the gap size are considered in the parametric investigation. Based on the analysis results reducing the yielding length of HBRB increases its post-yield stiffness and the axial strain and stress of the H-section core. Since buckling of the unconstrained region was observed in HBRBs with insufficient stiffener thickness, an analytical method is proposed for evaluating the sufficiency of stiffeners by estimating the critical buckling load of HBRB as a three-segment stepped compression member.