A density functional theory is used to investigate adsorption of colloids on the surfaces grafted by polymers of different architectures, including linear, star, branched, and dendritic structures. In order to calculate the direct bonding connectivity integral, a new numerical algorithm is proposed for polymers with complex architecture. A good agreement of the calculated results and the simulation and experimental data in studying grafted hard chain brushes confirm that our approach does lead a correct prediction. Accordingly, adsorption of colloids in the negative exponential attractive surface was studied. The effects of grafting density, attractive strength, molecular concentration, and size on adsorption were considered. The contour maps of excluded rate show that a complex architecture of polymer chains is much more effective in preventing adsorption than linear polymer brush. The results also show that the grafting density and complex architecture are two key factors to prevent colloidal adsorption, while the surface attractive strength only exhibits slight effect on colloidal adsorption. For polymer brushes with complex architecture, the height of potential of mean force is strongly dependent on the colloidal size. The larger the size, the higher is the potential of mean force, which means that the larger colloidal molecules are harder to penetrate the brush. In short, to prevent colloidal adsorption, it is more suitable to use the polymer brushes with complex architecture.