Healable, electrically conductive materials are highly desirable and valuable for the development of various modern electronics. But the preparation of a material combining good mechanical elasticity, functional properties, and intrinsic self-healing ability remains a great challenge. Here, we design composites by connecting a polymer network and single-walled carbon nanotubes (SWCNTs) through host-guest interactions. The resulting materials show bulk electrical conductivity, proximity sensitivity, humidity sensitivity and are able to self-heal without external stimulus under ambient conditions rapidly. Furthermore, they also possess elasticity comparable to commercial rubbers.