Display omitted •A re-centering energy-dissipation brace with a pendulum (REBP) is proposed.•The REBP can dissipate energy by friction and re-center the structure once unloaded.•Five REBPs with different cable tensions are subjected to cyclic loading tests.•The cable pretension has significant effects on the seismic behaviors of the REBP.•A hysteretic model and design formulas for the REBP are proposed and validated. In this study, a re-centering energy-dissipation brace with a pendulum (REBP) is proposed for high-rise structures. The REBP can consume energy by friction under the action of a horizontal external load, and then re-center the structure by means of cable pretension after removing the load. Through the lever action of the pendulum, the deformation capability of the REBP is significantly amplified with the small deformation of the cables, and can satisfy the inter-story drift requirement for a severe earthquake. The REBP is optimized from a prestressed re-centering energy-dissipation brace (PTSEB) previously proposed by the authors. In particular, the T-shaped pendulum in the PTSEB is replaced by a truss pendulum. The pendulum-wing, vertical bar, and diagonal bars form a truss with high strength. This increases the initial stiffness and energy consumption capability of the REBP, and decreases the weight of the REBP. Two semicircle rollers are set on the top and bottom of the blocker to facilitate its rotation. An hysteretic model and design formulas are proposed for the REBP. Through cyclic testing and a finite element (FE) analysis of REBPs with five different cable pretensions, the cyclic behaviors of the REBP and the influences of cable pretension on the energy consumption, re-centering, stiffness, friction, and cable tension are determined. The results indicate that the REBP has good energy consumption and a good re-centering capability. An increase in cable pretension leads to an increases in the friction between the blocker and pendulum-wing, energy consumption capability, and stiffness.