Quantum chemical calculations were carried out to investigate the hydrolysis reaction of GTP --> GDP by Gialpha1. Gialpha1 is one kind of G protein and contains a GTPase-activating protein (GAP) inside it. The reason for the increase in GTPase activity in the presence of GAP was examined in detail. Geometry optimization was performed at the Hartree-Fock level using the 3-21G** basis functional set. The energy levels required for all optimized structures of stable and transition states were re-estimated by the density functional theory (B3LYP) method using the 6-31G** basis set. It was revealed that the GTP --> GDP hydrolysis reaction proceeds through a proton relay process assisted by a Lys residue. This reaction is a one-step reaction and gives an activation-energy barrier of 35 kcal/mol. A Gln residue, a part of GAP, plays a role in maintaining the position of an H2O molecule near the gamma-phosphate of GTP, and the H2O molecule is therefore kept in an appropriate position for initiating the hydrolysis.