By using the density functional theory, we have studied the electronic structure and magnetism of the oxygen vacancy defect in GdCoO3 perovskite compound. We have carried out a magnetic stability calculation; between many possible magnetic configurations, the ferromagnetic ordering was predicted in both gadolinium and cobalt sublattices. We have demonstrated that the oxygen vacancy defect causes a ferromagnetic order via a mixture of octahedral HS Co3+, tetrahedral HS Co2+ and octahedral IS Co3+. From the spin magnetic moment and partial density of state investigation, we have predicted an induced long-range ferromagnetic ordering in nonstoichiometric GdCoO3−δ.