Morphology, structure and magnetic properties of nanocomposites of magnetite (Fe3O4) nanoparticles and alginic acid (AA) are studied. Magnetite Fe3O4 nanoparticles and the nanoparticles capped with alginic acid exhibit very distinct properties. The chemical bonding between alginic acid and surface of magnetite nanoparticles results in recovery of surface magnetization. On the other hand, it also leads to enhanced surface spin disorder and unconventional behavior of magnetization observed in Fe3O4-AA nanocomposites at low temperatures.