To simplify the construction of traditional self-centering buckling-restrained braces (SC-BRBs) and achieve efficient recovery function, an innovative type of single-tube self-centering buckling-restrained braces (ST-SC-BRBs) is proposed. The ST-SC-BRBs only require one outer tube for the prestressed system. The detailed structure and working principle of the ST-SC-BRBs are described, and it is emphasized that the restrained steel tube should be checked as a compression-bending member to ensure its overall stability. Low-cycle fatigue tests are conducted on scaled models of one traditional BRB and two ST-SC-BRBs. The results show that the residual deformation of the ST-SC-BRBs is significantly reduced compared to that of the traditional BRB, with comparable energy dissipation capacity. The ST-SC-BRB works stably with a full hysteresis curve and an obvious “flag-shaped” pattern within the inter-story drift ratio of 2%. The self-centering ratio is the key factor affecting the recovery effect of the ST-SC-BRB. To achieve smaller residual deformation, the self-centering ratio is suggested to be greater than 1. Overall, the ST-SC-BRB presents a more simplified and effective approach to constructing a recoverable functional structure.