Fluid flow through packed beds of uniform spheres is studied by a parallel lattice-Boltzmann (LB) model. The packed beds are obtained from simulations based on discrete element methods and have a wide porosity range. The LB model is specially designed for particle systems and is validated by comparing the simulated and measured results under different conditions. The validated model is then used to study the effect of porosity on the internal fluid flow and quantify the drag force on particles in packed beds. The results suggest that both the Reynolds number and packing structure significantly affect the fluid velocity distribution. A correlation is demonstrated between the packing structure and the velocity distribution, especially for flows at low Reynolds numbers. Beds with large porosity subjected to relatively large (e.g. moderate) Reynolds numbers are prone to display a secondary peak in the probability distribution of the normalized velocity. The interaction forces between particles and fluid in packed beds are examined. As a result of the non-uniform structure and flow, the drag force on a single particle varies giving a probability distribution. Based on the simulated results, a new equation is proposed to estimate the mean drag force on particles, which is more accurate than the correlations in the literature.