For the first time, a complete all-atom molecular dynamics (MD) model of a virus, bacteriophage MS2, in its entirety, including a protein outer shell, native genomic RNA with necessary divalent ions, and surrounding explicit aqueous solution with ions at physiological concentration, was built. The model is based on an experimentally measured cryo-EM structure, which was substantially augmented by reconstructing missing or low-resolution parts of the measured density (where the atomistic structure cannot be fit unambiguously). The model was tested by a quarter of a microsecond MD run, and various biophysical characteristics are obtained and analyzed. The developed methodology of building the model can be used for reconstructing other large biomolecular structures when experimental data are fragmented and/or of varying resolution, while the model itself can be used for studying the biology of MS2, including the dynamics of its interaction with the host bacteria.