Ruthenium(II) complexes, [Ru(babp)(dmso)L], consisting of tetradentate square-planar ligand (babp = 6,6'-bis(benzoylamino)-2,2'-bipyridinato) and two monodentate axial ones, DMSO and L (L = dmso or heterocycles), were synthesized and structurally characterized using UV-vis, NMR, ESI-MS, and IR spectroscopies and X-ray crystallography. These complexes showed catalytic activity toward the oxygen-atom-transfer reactions, such as epoxidation, allylic oxidation, cleavage reaction of olefins, and sulfoxidation of thioethers, in the presence of oxidant, PhIO. The relationship between the coordination structure and the catalytic activities of [Ru(babp)(dmso)L] was investigated. The active species for the reaction was assigned to be a high valent Ru-v=O or Ru-VI=O species. The oxo ligand was generated from the ligand-exchange reaction involving the dmso attached to [Ru(babp)(dmso)L]. Some complexes having a labile ligand at an axial position gave a Ru-VI=O species as an active intermediate, and others having moderate coordinating one gave a Ru-v=O one. The. oxidation activities of these complexes were affected by the axial ligand, L, through the trans-influence.