Three approaches of computational chemistry [quantum mechanics (QM) calculations, docking, and molecular dynamics (MD) simulations] were used to investigate the redox cycle of bovine erythrocyte glutathione peroxidase from class 1 (GPx1, EC 1.11.1.9). The pKa calculations for two redox states of the active-site selenocysteine of GPx1 (selenol, Sec45-SeH, and selenenic acid, Sec45-SeOH) were estimated using a bulk solvent model (B3LYP-IEFPCM and B3LYP-CPCM-COSMO-RS). The calculated pKa values of Sec45-SeH and Sec45-SeOH were corrected via a simple linear fit to a training set of organoselenium compounds, which consisted of aliphatic selenols and aromatic selenenic acids with available experimental pKa values. Based on docking calculations, binding sites for both molecules of the cofactor glutathione (GSH) are described. MD simulations on the dimer of GPx1 have been performed for all chemical states of the redox cycle: without GSH and with one or two molecules of GSH bound at the active site. Conformational analyses of MD trajectories indicate high mobility of the Arg177 and His79 residues. These residues can approach the vicinity of Sec45 and take part in the catalytic mechanism. On the basis of the calculated data, new atomistic details for a generally accepted mechanism of GPx1 are proposed.