In this paper, we present the first ever theoretical Compton profiles and electron momentum densities along with energy bands and density of states of rare earth oxide CeO2. We have employed the linear combination of atomic orbitals method to compute these electronic properties. For this, we have applied local density approximation, generalized gradient approximation and recently developed second order generalized gradient approximation within the frame work of density functional theory. The energy band gap of CeO2 is found to be in good agreement with the available data. Theoretical anisotropies in Compton profiles along ,  and  directions are explained in terms of energy bands.