Steel concentrically braced frames inherently provide great strength and stiffness, and are widely used for seismic resisting systems in buildings. These include conventional buckling braced frames and buckling restrained braced frames. Although the latter can prevent brace buckling and provide ductile behavior, both types of braces provide no hysteretic damping at small drift levels and offer very limited post-yielding stiffness. This study proposes a new type of steel brace with a novel mechanism—the naturally buckling brace (NBB). The design combines high-strength and low-yield steels arranged in parallel with a specified initial eccentricity along the brace length, providing ductile seismic behavior. Six tests of various NBB models subjected to cyclic loading were conducted to examine the seismic performance of the proposed NBB. Two specimens out of the six achieved the characteristics intended for NBB. The test results showed that the NBB specimens with appropriate design parameters could achieve early yielding, or hysteretic damping, from around 0.11% story drift and prevent local buckling as well as deformation concentration up to a very large story drift (greater than 3%). A single NBB would provide an asymmetric hysteretic behavior, a large post-yielding stiffness in tension, and a ductile performance with stable energy dissipation. Further systematic studies of NBBs are needed to comprehensively evaluate the capacities and limitations of the NBBs, including the reliability of performance with repeated tests.