The friction and wear problem of the electrical contact system (ECS) is common in various electrical equipment. Once the electrical contact fails due to wear, the electrical system may not work normally, which brings serious safety risks. Surface texture has been shown to have a good potential to improve interface wear under no-current conditions, while few studies have been performed to study the relationship between surface texture and current-carrying tribological performance. In addition, graphene is also receiving attention in the field of electrical contact due to its high electrical conductivity. However, the wear consumption of graphene during the friction process limits its long-term role. Therefore, combining the ability of surface texture to reduce wear and the ability of graphene in conducting and lubrication, a texture-graphene composite surface (TS-G surface) is constructed. The effects of TS-G surfaces on the tribological properties of electrical contact surfaces are studied by comparing them with smooth surfaces (SS surfaces), textured surfaces (TS surfaces) and smooth-graphene surfaces (SS-G surfaces). The results show that TS-G can effectively reduce the friction coefficient (COF), and the COF stays at about 0.15 during the whole current-carrying friction process, and no visible fluctuation can be observed from the COF curve. In addition, the TS-G surface can effectively suppress the interface friction-induced vibration. More importantly, the TS-G surface has a good effect on the electrical contact stability. The surface topography analysis shows that the wear degree of the TS-G surface is quite slight, and the width of the wear track is only 30μm. The texture is found to be able to store graphene and continue to play the role of surface conduction and lubrication. The results of this study provide potential means for surface design to improve the stability of electrical contact.