A flexible, electrically conducting hydrogel with self-healing repeatability can be of use in emerging fields such as soft passive resistors-capacitors and electro-active soft sensor devices, but combining all these properties remains a challenging task. Here, we report a versatile hydrogel composite produced from commercial superabsorbent polymer and hyperbranched polymer with reduced graphene oxide (rGO) by a simple fabrication method. The composites show excellent electrical self-healing properties (completely healed after 20 seconds) with ultra-high water-absorption ability of up to 350 times normal under ambient conditions. The composites possess excellent water-absorption reusability and the water-absorption ability can be adjusted by changing the amounts of rGO and hyperbranched polymer in the composites. The electrical conductivity can also be modified by varying the amount of absorbed water, and the product would be a good candidate for soft moisture-related resistors-sensor systems.