The local structure of cellulose, dissolved in the frequently used ionic liquid EMIm-OAc, is modelled by a coaxial double layer cylinder. The cylinder’s core consists of a cellulose chain while the sheath is formed by a solvent layer with lower electron density than the bulk solvent. We studied 2% cellulose solutions in EMIm-OAc and their behavior upon addition of increasing amounts of water. At this cellulose concentration, 15 wt% of water induced the precipitation of cellulose. Water molecules did not form an independent phase, but were bound to EMIm-OAc in the cellulose/water/EMIm-OAc solution. The conformational of a cellulose chain changes by adding water into the solution, and the square of the apparent cross-sectional radius of gyration of the cellulose chain becomes zero to negative. This phenomenon is explained by the formation of a solvation shell with lower electron density than the bulk solvent around the cellulose chain.