The adsorption of toxic heavy metal cations, i.e,, Cu(II), Cd(II), and Pb(II), from metal-EDTA mixture solutions on a composite adsorbent having a heterogeneous surface, i.e., bauxite waste red mud, has been investigated and modeled with the aid of a modified surface complexation approach in respect to pH and complexant dependency of heavy metal adsorption. EDTA was selected as the modeling ligand in view of its wide usage as an anthropogenic chelating agent and abundance in natural waters. The adsorption experiments were conducted for metal salts (nitrates), metal-EDTA complexes alone, or in mixtures containing (metal + metal-EDTA). The adsorption equilibrium constants for the metal ions and metal-EDTA complexes were calculated. For all studied cases, the solid adsorbent phase concentrations of the adsorbed metal and metal-EDTA complexes were found by using the derived model equations with excellent compatibility of experimental and theoretically generated adsorption isotherms. The model was useful for metal and metal-EDTA mixture solutions either at their natural pH of equilibration with the sorbent, or after pH elevation with NaOH titration up to a certain pH. Thus adsorption of every single species (M2+ or MY2-) or of possible mixtures (M2+ + MY2-) at natural pH or after NaOH titration could be calculated by the use of simple quadratic model equations, once the initial concentrations of the corresponding species, i.e., [M2+](0) or [MY2-](0), were known. The compatibility of theoretical and experimental data pairs of adsorbed species concentrations was verified by means of nonlinear regression analysis. The findings of this study can be further developed so as to serve environmental risk assessment concerning the expansion of a heavy metal contaminant plume with groundwater movement in soil consisting of hydrated-oxide type minerals.