Hydrogen bonds play critical roles in non-covalent directional interactions determining the crystal structure of cellulose. Although diffraction studies accurately determined the coordinates of carbon and oxygen atoms in crystalline cellulose, the structural information on hydrogen atoms involved in hydrogen-bonding is still elusive. This could be complemented by vibrational spectroscopy; but the assignment of the OH stretch peaks has been controversial. In this study, we performed calculations using density functional theory with dispersion corrections (DFT-D2) for the cellulose I beta crystal lattices with the experimentally determined carbon and oxygen coordinates. DFT-D2 calculations revealed that the OH stretch vibrations of cellulose are highly coupled and delocalized through intra- and interchain hydrogen bonds involving all OH groups in the crystal. Additionally, molecular dynamics (MD) simulations of a single cellulose microfibril showed that the conformations of OH groups exposed at the microfibril surface are not well-defined. Comparison of the computation results with the experimentally determined IR dichroism of uniaxially aligned cellulose microfibrils and the peak positions of various cellulose crystals allowed unambiguous identification of OH stretch modes observed in the vibrational spectra of cellulose.