Compared to concrete or mortar-filled Buckling-Restrained Braces (BRBs), all-steel BRBs provide weight and fabrication time reductions. In particular, all-steel buckling braces with H-section cores are gaining attention in cases where large axial strength is required. In this paper, an all-steel BRB, called NOVEL (Noise, CO2 emission, Vibration, Energy dissipation and Labor), is presented. It comprises an H-section core encased in a square casing, and its behavior was studied through full-scale subassembly and brace tests, followed by a finite element parametric study. Two failure modes were observed: global buckling and flange buckling of the H-section core, which occurred in test specimens with Pcr/Py ratios of 1.68 and 4.91, respectively. Global buckling occurred when the maximum moment in the casing reached its yielding moment, although the test specimens had sufficient stiffness to prevent global buckling. Failure by core flange buckling occurred at a core strain of 1.2%. The finite element parametric study indicated that adjusting the width-to-thickness ratio of the core flange is more feasible than stiffening the flange or adjusting the unconstrained-length end stiffeners. The value of 5.06 was the minimum flange slenderness ratio that provided a stable hysteresis to the end of the loading protocol of the American Institute of Steel Construction standard.