Freshwater scarcity is one of the major challenges facing the world today. Atmospheric water harvesting (AWH) technologies, especially adsorption-based AWH, offer a promising solution for arid regions. At present, it is still challenging to develop adsorbents that combine high water absorption, excellent mechanical strength, salt leakage prevention, and efficient solar-driven water release properties. In this study, a novel wood-grafted hydrogel composite (SACL@W) has been developed, using cellulose wood (W) as a three-dimensional skeleton, sodium alginate hydrogel (SA) as a carrier to immobilize the hygroscopic salt LiCl (L), and carbon nanotubes (C) to provide high efficiency of solar-thermal conversion. With the wood support, SACL@W has a high compressive strength of up to 1.14 MPa and remains largely stable in 10 compression cycles. The saturated water absorption is up to 3.36 g/g at 20 degrees C and 80% relative humidity (RH). Under solar irradiation of 1000 W/m2, the water release rate reaches 1.327 g/(g h), with near-complete (similar to 99%) water release in 3 h. The AWH performance is stable over 10 cycles of uptake-release, with a capacity of up to 0.69 g/g per cycle. A simple device is developed for AWH to collect about 0.6 g/g of liquid water, and the quality of the collected water complies with the World Health Organization's standards for domestic water use. The composite material provides a new strategy for the development of highly efficient, stable, and sustainable solar-driven AWH materials, with potential applications in alleviating the water scarcity in arid regions.