Buckling-restrained braces (BRBs) have been widely used in engineering practice in recent years due to their excellent energy dissipation capability. However, the property of the low post-yield stiffness observed in BRBs may result in interstory drift concentration, accompanied by large residual drifts when used in moment-resisting frames. To address this issue, a novel multi-stage yielding energy dissipation brace is proposed to improve the limitations mentioned above of the BRBs. The core elements of the novel energy dissipation brace are steel U-shaped dampers (UDs), which have the advantages of stable energy dissipation capacity, good fatigue resistance, and superior plastic deformation capability. The working mechanism of the novel multi-stage yielding energy dissipation brace was described first. To demonstrate the effectiveness of the novel brace, three braces were designed and these hysteretic properties were validated by finite element models. The numerical results show that the simulated hysteresis loops exhibit two yielding stages under cyclic loading. The increased post-yield stiffness of the novel braces provides a promising solution for reducing the residual drifts of moment-resisting frames under strong earthquakes.