Cellulose is an important biocompatible and nontoxic polymer widely used in numerous biomedical applications. The impact of cellulose-based materials on cells and, more specifically, on plasma membranes that surround cells, however, remains poorly understood. To this end, here, we performed atomic-scale molecular dynamics simulations of phosphatidylcholine (PC) and phosphatidylethanolamine (PE) bilayers interacting with the surface of a cellulose crystal. Both biased umbrella sampling and unbiased simulations clearly show the existence of strong attractive interactions between phospholipids and cellulose: the free energy of the cellulose-bilayer binding was found to be -1.89 and -1.96 kJ/mol per cellulose dimer for PC and PE bilayers, respectively. Although the values are similar, there is a pronounced difference between PC and PE bilayers. The driving force in both cases is the formation of hydrogen bonds. There are two distinct types of hydrogen bonds: (1) between the lipid head groups and the hydroxyl (hydroxymethyl) groups of cellulose, and (2) lipid-water and cellulose-water bonds. The former is the dominant component for PE systems whereas the latter dominates in PC systems. This suggests that achieving controlled binding via new cellulose modifications must pay close attention to the lipid head groups involved. The observed attractive phospholipid-cellulose interactions have a significant effect on bilayer properties: a cellulose crystal induces noticeable structural perturbations on the bilayer leaflet next to the crystal. Given that such perturbations can be undesirable when it comes to the interactions of cellulose-based materials with cell membranes, our computational studies suggest that the impact of cellulose could be reduced through chemical modification of the cellulose surface which prevents cellulose-phospholipid hydrogen bonding.