A computational fluid dynamics model was developed for gas-solid fluidized beds containing a mixture of two particle species. To calculate stresses of the solid phase, the kinetic theory of granular flow was extended to consider a binary mixture of smooth, nearly elastic, spheres. The developed model was simulated to demonstrate key features of binary mixture fluidization. Bed expansion with a binary mixture of different size particles, but with identical densities, was much higher than that of a system consisting of mono-sized particles of the same mean size as the bimodal mixture. Minimum fluidization velocity for the binary particle system was significantly lowered. The mixing behavior of the binary mixture of particles, characterized by the mixing index, increased with increasing superficial gas velocity. For a binary mixture of particles of larger size with lower density and smaller size with higher density, larger, lighter particles segregated to the top of the fluid bed, while smaller, heavier particles segregated to the bottom. With increasing fluidization velocity, this segregation pattern reversed and inversion occurred. The drag and gravity force difference between small, heavy particles and large, light particles was dominant at low gas velocities. With an increase in gas velocity, however, the gradients in granular temperature and pressure became dominant terms in the equations for the relative force and thus velocity between two different particle species.