The cellodextrins in native crystalline cellulose Iα and Iβ are unusually stable compared to other polysaccharides, not easily prone to hydrolysis even with chemical or biological catalysts. The stability of crystalline cellulose Iβ is most likely due to its greatly enhanced hydrogen-bonding (HB) network. We carried out ab initio calculations to determine the native crystalline cellulose Iβ atomic and conformational structures. For bulk crystalline cellulose, we found that every hydroxyl group in the cellulose structure is hydrogen bonded both as a donor and acceptor. This agrees well with published x-ray and neutron diffraction data. We also determined the electronic structures and the energetics for one cellodextrin chain, one to four sheets of cellodextrins in cellulose, and the bulk cellulose Iβ. It was found that both the HOMO and LUMO orbital energies increase as the size of the crystal becomes larger, whereas the change of band-gap is not significant. A theoretical model based on the competition between hydrogen bonding energy and strain energy was constructed to explain the size of native cellulose Iβ.