We study the metal-insulator transition in a model Mott system, a bcc hydrogen solid, by performing ab initio quasiparticle band-structure calculations within the GW approximation for a wide range of lattice constants. The value of the critical electron density n(c) is consistent with Mott's original criterion. For smaller lattice constants, our spin-polarized GW results agree well with previous variational quantum Monte Carlo calculations. For large lattice constants, the computed quasiparticle band gap corresponds to the difference between the ionization energy and electron affinity of an isolated hydrogen atom. Near the metal-insulator transition, we investigate the quality of the quasiparticle wave functions obtained from different starting approximations in density-functional theory. Finally, we gain new insight into the GW method and its applicability to spin-polarized systems, for which several refinements are introduced.