The cellodextrins in native crystalline celluloses are unusually stable compared to other polysaccharides, not easily prone to hydrolysis even with chemical or biological catalysts.  The stability of crystalline cellulose is most likely due to its highly cooperative hydrogen-bonding (HB) network.  We carried out ab initio calculations to determine the atomic and conformational structures of native crystalline celluloses and for cellulose polymers with degree of polymerization varying from 2 to 7.  A highly cooperative hydrogen bonding interaction was found in these cellulose structures.  The average hydrogen bonding interaction energy is found to be enhanced by more than 50%.  The origin of this cooperativity will be discussed based on the charge transfer and electrostatic interaction models.