Montmorillonite layer edge surfaces have pH-dependent properties, which arises from the acid-base reactivity of their surface functional groups. Edge surface acidity (with intrinsic reaction equilibrium constant, pKa) is a chemical property that is affected by crystal structure. While a cis-vacant structure predominates in natural montmorillonites, prior molecular-level studies assume a centrosymmetric trans-vacant configuration, which potentially leads to an incorrect prediction of montmorillonite acid-base surface properties. We computed intrinsic acidity constants of the surface sites of a montmorillonite layer with a cis-vacant structure using the first-principles molecular dynamics-based vertical energy gap method. We evaluated pKa values for both non-substituted and Mg-substituted layers on common edge surfaces (i.e., surfaces perpendicular to [010], [01̅0], [110], and [1̅1̅0] crystallographic directions). The functional groups ≡Si(OH), ≡Al(OH2)2/≡Al(OH)(OH2), and ≡SiO(OH)Al sites on surfaces perpendicular to [010] and [01̅0] and ≡Si(OH)U, ≡Si(OH)L, ≡Al(OH2), and ≡Al(OH2)2 on surfaces perpendicular to [110] and [1̅1̅0] determine the proton reactivity of non-substituted cis-vacant edge surfaces. Moreover, the structural OH sites on edge surfaces had extremely high pKa values, which do not show reactivity at a common pH. Meanwhile, Mg2+ substitution results in an increase in pKa values at local or adjacent sites, in which the effect is limited by the distance between the sites. A surface complexation model was built with predicted pKa values, which enabled us to predict surface properties as a function of pH and ionic strength. Edge surface charge of both trans- and cis-vacant models has little dependence on Mg2+ substitutions, but the dependence on the crystal plane orientation is strong. In particular, at pH below 7, edge surfaces are positively or negatively charged depending on their orientation. Implications of these findings on contaminant adsorption by smectites are discussed.