We investigate the electronic and magnetic properties in Cu-doped InN with the N vacancy ($V_N$) from first principles calculations. There is the long-range ferromagnetic order between two Cu atoms, attributed to the hole-mediated double exchange through the strong p-d interaction between the Cu atom and neighboring N atom. The system of $V_N$ defect in Cu-doped InN has the lowest formation energy. Due to the hybridization between the Cu-3d and $V_N$ states, the spin-polarization on the Cu atoms in the InN lattice is reduced by $V_N$ defect. So, it shows a weak ferromagnetic behavior.