This paper presents a novel type of hybrid self-centering braces incorporating tension-only superelastic NiTi shape memory alloy (SMA) cables and integrated viscoelastic dampers (VEDs). One of our reasons for proposing this new SMA-viscoelastic hybrid brace (SCVEB) is to provide enhanced energy-dissipation ability whilst promoting increased self-centering tendency compared with the existing SMA-based self-centering solutions, where upgrading behavior is mainly benefited from the participation of the VEDs. The configuration and the working principle, along with theoretical equations describing the mechanical behavior of the SCVEB, are described in detail firstly. Experimental verification of individual elements in this SCVEB system, namely the NiTi SMA cables and VEDs, was performed to obtain a basic understanding of their mechanical properties. A proof-of-concept SCVEB specimen was then manufactured, and its cyclic performance was further investigated. Followed by this, a system-level analysis on a series of steel frames equipped with or without SCVEB was conducted. The results showed that the SCVEB system exhibited a moderate damping ratio and a more efficient controlled behavior in terms of its post-event residual deformation and floor acceleration when compared with those of the non-SCVEB system.