The conventional covalently cross-linked double network (DN) hydrogels with high stiffness often show low toughness and self-healing property due to the irreversible bond breakages in their networks. Therefore, scarcity of hydrogels that possess simultaneous features of stiffness, toughness, and autonomous self-healing properties at the same time remains a great challenge and seriously limits their biomedical applications. While, many natural materials acquire these features from their dynamic sacrificial bonds. Inspired by biomaterials, herein we propose a novel strategy to design stiff, tough and self-healing DN gels by substitution of both covalently cross-linked networks with strong, dynamic hydrogen bond cross-linked networks. The prepared fully physically cross-linked DN gels composed of strong agar biopolymer gel as the first network and tough polyvinyl alcohol (PVA) biopolymer gel as the second network. The DN gels demonstrated multiple-energy dissipating mechanisms with a high modulus up to 2200kPa, toughness up to 2111kJm, and ability to self-heal quickly and autonomously with regaining 67% of original strength only after 10min. The developed DN gels will open a new avenue to hydrogel research and holds high potential for diverse biomedical applications, such as scaffold, cartilage, tendon and muscle.