A buckling-restrained brace (BRB) serves as a typical load-bearing and energy-dissipative device for the passive control of structures under seismic loading. A BRB is generally designed to not yield under frequently occurring earthquake (FOE) and wind loads, resulting in it having less effectiveness in vibration reduction compared with post-yielding performance. To address this dilemma, this study proposed the concept and technique details of the viscoelastic-yielding compounded BRB (VBRB). Different from a conventional BRB, a VBRB is fabricated by attaching the viscoelastic damper (VED) to the surface of a BRB’s steel casing, ensuring a compatible deformation pattern between the VED and the BRB’s steel core. A dynamic loading test of VBRB specimens was carried out in which 0.2 Hz~0.6 Hz in loading rate and a maximum of 550 kN in load-bearing capacity had been applied, verifying the feasibility and performance of the VBRB. Subsequently, a parametric design procedure was developed to determine the required VBRB parameters so that the maximum elastic drift response of the structure could be reduced to the code-prescriptive value. The wind-resistance and seismic performances of the VBRB were critically evaluated through dynamic time-history analyses on a 48-story mega VBRB-equipped frame designed according to the Chinese seismic design code (GB50011-2010), and the effectiveness of the approach was also verified. Results indicate that the VBRB has advantages over a conventional BRB by providing a multi-stage passive energy dissipation capacity, resulting in a better vibration-control effect than conventional BRBs for structures subjected to wind load and seismic excitations.