As a step toward understanding the electronic and the magnetic properties of CoO nanocrystals, we carried out first-principles calculations of wurtzite CoO by using the local density approximation +U (LDA+U) density functional method. The total energy, electronic structure, and magnetic properties were calculated and compared to those of conventional rock-salt-type Co oxides. In contrast to the previous local spin density approximation (LSDA) calculation result, the wurtzite CoO is found to be a Mott insulator with antiferromagnetic spin ordering in its ground state, similar to the case of rock-salt CoO. This suggests that the wurtzite phase of CoO is not responsible for the observed magnetic signal from CoO nanocrystals.