The combination of organic matter, iron oxide, and clay minerals is of great significance for the adsorption of copper ions (Cu). The purpose of this study is to explore the characteristics of Cu adsorption and laws governing Cu complexation to organic–inorganic, organic–clay mineral, and iron-oxide–clay mineral complexes in the sediments in the estuary of plateau fault and sinking lake——Dianchi Lake. In this study, Cu adsorption tests were performed on the three complexes, in order to study the kinetic behavior of adsorption, Langmuir and Freundlich isotherm models were used. The samples before and after adsorption were characterized via scanning electron microscope (SEM), Fourier infrared spectroscopy (FTIR), and X-ray diffraction (XRD). Our results show that, the Freundlich isotherm models model was able to describe adsorbent behavior in comparison to the Langmuir models. During the Cu adsorption process, the iron-oxide–clay mineral complex is able to adsorb Cu, via coordination exchange, through the –OH contained therein. Organic-matter–clay mineral complexes bonded to the surfaces of clay minerals by replacing the hydroxyl groups with functional groups (carboxyl groups or phenolic hydroxyl groups) contained in the organic matter. Organic–inorganic composites then adsorbed Cu through the coordination exchange of –OH in the polar functional groups of alcohols, phenols, and carboxylic acids. The adsorption capacity of Cu in these three sediment complexes was observed to have the following order: organic–inorganic complex > organic-matter–clay mineral complex > iron-oxide–clay mineral complex. The semi-quantitative analysis results of Fourier Infrared Spectroscopy show that the organic matter (changes in the peak area of functional groups such as carboxyl groups) in the organic-inorganic composite material has an important effect on the amount of copper ions adsorbed by clay minerals.