Chemical modification of silver nanoparticles (AgNPs) with a stabilizing agent, such as poly(vinyl alcohol) (PVA), plays an important role in shape-controlled seeded-growth and colloidal stability. However, theoretical aspects of the stabilizing mechanism of PVA are still poorly understood. To gain a better understanding of the role of PVA in water protecting effects for silver nanoparticles, we developed an atomistic model of a AgNP grafted with single-chain PVA of various lengths. Our model, designed for classical molecular dynamics (MD) simulations, approximates the AgNP as a quasi-spherical silver nanocrystal with 3.9 nm diameter and uses a united-atom representation for PVA with its polymer chain length varying from 220 up to 1540 repeating units. We found that PVA adsorbs onto the AgNP surface through multiple non-covalent interactions, among which non-covalent bonding of the hydroxyl groups plays a key role. The analysis of adsorption isotherms by using the Hill, Scatchard, and McGhee & von Hippel models exhibits evidence for positive binding cooperativity with the cooperativity parameter varying from 1.55 to 2.12. Our results indicate that the size of the PVA polymer rather than its structure plays a crucial role in providing water protecting effects for the AgNP core, varying from 40% up to 91%. The water-protecting efficiency was well approximated by the Langmuir–Freundlich equation, allowing us to predict that the saturated coverage of the nanoparticle of a given diameter of 3.9 nm should occur when the PVA molecular weight approaches 115 kDa, which corresponds to the number of vinyl alcohol monomers being equal to 3100 units.