Formation behavior of PEO (Plasma Electrolytic Oxidation) films on AZ31 Mg alloy was studied in aqueous solutions containing various concentrations of hydroxide ion ($OH^-$) and silicate ion ($SiO_3{^{2-}}$) by voltage-time curves, and corrosion resistance of the PEO film-covered specimen was investigated by immersion test in 0.5 M NaCl solution. From the analyses of the voltage-time curves, it is suggested that two different types of anions are essentially needed for the formation of PEO films on AZ31 Mg alloy: film formation agent and local film breakdown agent. $SiO_3{^{2-}}$ ion acts only as a film formation agent but $OH^-$ ion acts not only as a film formation agent but also film breakdown agent. The PEO films prepared on AZ31 Mg alloy in alkaline silicate solution showed very good corrosion resistance without any pitting or filiform corrosions up to 480 h of immersion in 0.5 M NaCl.