The kinetic theory for particles of equal mass, density, and size is well established. However, kinetic theory for particles of different density and size is yet to be established. In this paper, the balance laws and constitutive relations for a granular mixture with particles of different size and densities are derived. The computed results indicate significant changes when compared with the theory that is derived by assuming particles of equal size and density. A comparison of the proposed theory with the theories given by Manger [Modeling and simulation of gas solid systems in curvilinear coordinates. PhD Thesis, Telemark Institute of Technology, Norway, 1996] and Huilin et al. [Physica, A, 284 (2000) 265] has also been made.