In this paper, we present a hybrid model for the numerical assessment of poly-disperse gas-solid fluidized beds. The main idea of such a modeling strategy is to use a combination of a Lagrangian discrete phase model (DPM) and a kinetic theory based TFM to take advantage of the benefits of those two different formulations. On the one hand, the local distribution of the different particle diameters, which is required for the gas-solid drag force, can be obtained by tracking statistically representative particle trajectories for each particle diameter class. On the other hand, the contribution from the inter-particle stresses, i.e. inter-particle collisions, can be deduced from the TFM solution. These then appear as additional body force in the force balance of the DPM. Note that in a first step we solely consider diameter averaged solids stresses since the drag force is at least on order of magnitude higher than the solids stresses in fluidized beds. Finally, the numerical model is applied to a fluidized bed of a bi-disperse mixture of glass particles (0.5 mm and 2.5 mm particles) and with a cross-section of 0.15 m x 0.02 m. The results are then analyzed with respect to experimental data of Puttinger et al [1]. This comparison demonstrates that the computed bed hydrodynamics is in fairly good agreement with the experiment. However, the results also suggest that sub-grid drag corrections [2-4] for polydisperse fluidized beds are required to make the numerical investigation of industrial scale fluidized bed units accessible.