The flocculation of colloidal particles by adsorbing polymers is one of the central issues of colloid science and a very important topic in many industrial, biological, and environmental processes. We report a computer simulation study of 2- and 3-dimensional model for bridging flocculation between large linear polymer chains and comparatively small colloidal particles, where the structure and growth kinetics of cluster formation are investigated. This model was developed within the framework of the cluster-cluster aggregation model using mass and fractal dimension dependent diffusion constants, where bridging flocculation is seen as a case of heterocoagulation in which, in addition, macromolecule configurations and lengths play an important role. The simulation of aggregate structure and formation kinetics obtained at different (i) relative particle concentrations, (ii) polymer chain conformations, and (iii) sticking probabilities are described from a qualitatively and quantitative point of view. The results suggest that the formation of large aggregates is a slow process, controlled by the reactivity of the clusters, even when the reaction between microcolloids and macrochains is very fast. Aggregation kinetics are strongly dependent on the particle/ chain concentration ratio and on the configurational properties of the chains. It is shown that the scaling laws which are valid for homocoagulation processes are also applicable to the kinetics of bridging flocculation. The corresponding scaling exponents have been calculated.