We studied the effect on the electronic and magnetic properties of the N defect in clean and Cu-doped wurtzite III-nitrides by using the first-principles calculations. When it is doped two Cu atoms in the nearest neighboring sites, the system of AlN, GaN, or InN with the N vacancy is energetically more favorable than that without the N vacancy site. When the Cu concentration increases, the total magnetic moment of a supercell becomes small. The ferromagnetism of Cu atom is very low due to the weak 3d-3d coupling. It is noticeable that the spin-exchange interaction between the Cu-3d and N defect states is important.