International audienceWe present ab initio quasiparticle calculations for electronic excitations and the fundamental band gap of the strongly correlated transition-metal oxide CuO using the GW approximation of many-body perturbation theory. Problems related to the suitability of the method for strongly correlated materials and issues of self-consistency are addressed. We explain why quasiparticle self-consistent GW strongly overestimates the band gap of CuO. Apart from the band gap, electron addition and removal spectra in the quasiparticle approximation including lifetime and matrix-element effects are found to be in excellent agreement with the quasiparticle excitations in direct and inverse photoemission data