Generally, Ag and N can be taken as relatively better candidates for p-type ZnO. In this letter, we investigate the electronic structures and optical properties of N- or Ag-doped ZnO with F as the reactive donor. F atom is found to not only enhance acceptor solubilities, but also lower acceptor levels in the band gap of co-doped ZnO. In addition, we analyze the imaginary portion of the dielectric functions, refractive indices, and loss functions for pure and co-doped ZnO. A comparison with pure ZnO shows that the remarkable feature for these co-doped ZnO is a strong absorption in the visible light region, indicating that they could be taken as the potential candidates for photocatalytic material.