Balance laws and constitutive relations for a binary granular mixture with unequal granular temperature are derived. The complete pair distribution function for two colliding spheres was assumed to be the product of Maxwellian velocity distributions for each phase. The constitutive relations together with the transport equations form a model for a binary granular mixture with unequal granular temperature. An analytical expression for viscosity of each phase shows the effect of different masses and granular temperatures of particles