Using first-principles calculations based on density functional theory within GGA formalism, we have studied the electronic structure and magnetic properties of (Ga,Co) co-doped ZnO system. The effect of impurity distances on ferromagnetic and antiferromagnetic ground state in Co0.056Zn0.944O has been studied. For the closest Co-Co distance, a ferromagnetic ground state with total magnetic moment of ∼⃒3.00μB per Co atom has been found. The electronic structure also displays a nearly halfmetallic order. Conversely, for the farthest Co-Co distance an antiferromagnetic ground state was found for Co0.056Zn0.944O. When Zn2+ ions are replaced by Ga ions in Co0.056Zn0.944O, the new (Ga,Co) co-doped ZnO system is more energetically stable. It has also been found that Ga-doping reduces the Co0.056Zn0.944O band gap due to the sp-d exchange interactions, which is in good agreement with the experimental data. Moreover, the Ga-doping changes the nearly halmetallic order of Co0.056Zn0944O to metallic. Results also show that Ga0.029Co0.056Zn0.915O is still ferromagnetic with a total magnetic moment of ∼⃒3.00μB per Co atom. It was also found that the ferromagnetic ground state in (Ga,Co) co-doped ZnO vanishes as Ga concentration increases.