Due to their high mechanical properties and recoverability, hybrid double-network (DN) hydrogels composed with a physically cross-linked network (the first network) and a chemically cross-linked network (the second network) arouse researchers' interest and attention in various fields. In this work, we have fabricated hybrid double-network hydrogels with ionically cross-linked kappa-carrageenan as the first network and covalently cross-linked poly(N-acryloyl glycinamide) (PNAGA) as the second network by using an one-pot method. Because of synergistic interaction between kappa-carrageenan and PNAGA polymer chains, the hybrid DN hydrogels exhibit excellent mechanical properties with a breaking stress of 1.7 MPa and a breaking strain of 250%, which are much better than their parent single-network hydrogels. In addition, due to the physical cross-links among kappa-carrageenan and PNAGA, the hybrid DN hydrogels show good self-healing ability; and due to the biocompatibility of all components, the hybrid DN hydrogels show low cytotoxicity. All those properties endow the potential application of kappa-carrageenan/PNAGA DN hydrogel in bioengineering.