This study explores a novel type of SMA-Friction Self-centering Brace (SFSCB) composed of Ni-Ti shape memory alloy (SMA) cables and Friction pads. The SFSCB functions as a hybrid damper, operating on a mechanism where SMA cables and frictional components are arranged in parallel to synergistically provide energy dissipation and self-centering capabilities. In the paper, the configuration and basic working principle of the proposed brace are presented first, highlighting its advantages over existing SMA-based hybrid braces. To validate the hysteretic characteristics of the SFSCB, test specimens were fabricated and subjected to a series of cyclic loading tests. These tests considered various factors affecting performance, including training effects and pre-pressure levels. The experimental results indicate that the brace exhibits a symmetrical tension-compression flag-shaped hysteresis curve. Compared to existing types of SMA-based braces, the SFSCB demonstrates superior self-centering and energy dissipation capabilities, making it a promising device for seismic applications in structural engineering.