Heavy metal pollution is a global problem affecting the environment and human health. Sediment is the source sink of heavy metals in water. Under certain circumstances, the migration of heavy metals will cause water pollution. Therefore, it is of great significance to study sediment composition and composite complexes in the migration and transformation of heavy metals. To understand the adsorption mechanisms of composite complexes and improve the theoretical understanding of adsorption in multi-component complex systems, this study explored the characteristics and rules of Cu adsorption to organic–inorganic, inorganic minerals, and iron-oxide–clay complexes in the estuary sediments of the Dianchi Lake. The Langmuir and Freundlich isotherm models were used for Cu adsorption experiments on three complexes to study their adsorption kinetics. X-ray diffraction and Fourier transform infrared spectroscopy characterized the samples before and after adsorption. The relationship between adsorption capacity and sediment composition was analyzed through redundant analyses. The results showed that the Freundlich isothermal model was better than the Langmuir model in describing the adsorption behavior of the adsorbents. The contribution of iron and aluminum oxides to Cu adsorption was more than that of organic matter. The organic–inorganic complexes functional groups involved in copper adsorption are the most, which resulting in a higher adsorption capacity. The organic matter removal (organic degradation in sediment) will reduce the polar functional groups and reduce silicide activity, leading to heavy metal desorption and re-entry into the water body.