In this work, anodic oxidation behavior of AZ31 Mg alloy was studied as a function of $Na_2CO_3$ concentration in electrolyte by voltage-time curves and observation of surface appearances and morphologies after the anodic treatments, using optical microscopy and confocal scanning laser microscopy (CSLM). The voltage-time curves of AZ31 Mg alloy surface and surface appearances after the anodic treatments showed three different regions with $Na_2CO_3$ concentration : region I, below 0.2 M $Na_2CO_3$ where shiny surface with a number of small size pits; region II, between 0.4 M and 0.6 M $Na_2CO_3$ where dark surface with relatively low number of large size burned or dark spots; region III, more than 0.8 M $Na_2CO_3$ where bright surface with or without large size dark spots were obtained. The anodically treated AZ31 Mg alloy surface became significantly brightened with increasing $Na_2CO_3$ concentration from 0.5 M to 0.8 M which was attribute to the formation of denser and smoother surface films. Pits and porous protruding reaction products were found at relatively large size and small size spots, respectively, on the AZ31 Mg alloy surface in low concentration of $Na_2CO_3$ less than 0.2 M. The formation of pits is attributed to the result of repetition of the formation and detachment of porous anodic reaction products. Based on the experimental results obtained in this work, it is concluded that more uniform, denser and smoother surface of AZ31 Mg alloy could be obtained at more than 0.8 M $Na_2CO_3$ concentration if there is no other oxide forming agent.