The extraction of water from air is a promising way to supply fresh water, especially in remote, arid regions. This process can be supported by desiccant materials such as zeolites, metal-organic frameworks, or hygroscopic salts. Here we present a composite material that is able to absorb 660 kg of water per cubic meter of bulk material from air at 10 mbar water vapor pressure and 28 degrees C. The material consists of calcium chloride incorporated into an alginate-derived matrix. A simple synthesis route leads to spherical beads of the composite with a diameter of approximately 2 mm. This macroscopic structure allows for good vapor permeability through packed beds. The collected water can be released at 100 degrees C, potentially enabling a solar-driven application. In addition, the synthetic route uses cheap, non-toxic, and easily accessible materials allowing for widespread application.