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The volume behaviour of cerium monoxide (CeO) is interesting as a function of pressure. The volume decreases rapidly up to 3 GPa and decreases more slowly above 3 GPa. The authors present the fully self-consistent band structure of CeO for four different values of lattice constant corresponding to four different pressures, using the linearised augmented plane-wave method. The local density formulation has been assumed for the exchange and correlation part of the potential. From the band-structure results, they have calculated the valency of Ce in CeO. The calculated valency increases from 3.0 to 3.26 with increase in pressure. From the band-structure results, the density of states, the coefficient of linear specific heat and the optical absorption spectra have been calculated.