Strong and tough hydrogels with good self-healing property and processability are of great interest in the recent decades, however, how to simultaneously realize high mechanical properties and self-healing performance still remains a challenge. Here, we report a fully physical dual-network (DN) hydrogel consisting of poly(acrylic acid) (PAA) network crosslinked by ferric ions and chitosan (CS) network crosslinked with calcium ions and chain entanglement. The resulting hydrogel displays a tensile strength of 12.2 MPa and a tensile strain of 1290%. Under the strain of 1000%, 35.7 MJm(-3) of energy can be dissipated by the hydrogel network. Due to the reversibility of the physical crosslinks, particularly, the hydrogel presents high self-recovery and self-healing performances, that is, its tensile strength is recovered to 2.3 MPa after healing. Additionally, even if fragmented, the hydrogel can still acquire a tensile stress of 4.3 MPa after re-processing. This finding indicates the effective strategy to construct high-performance hydrogels can bring benefits to more soft materials.