Electrode longevity, the cost of ion-exchange membranes, and side reactions are critical obstacles for desalination batteries to compete with traditional technologies. Anion-selective faradaic electrodes with antifouling and antidissolution properties remain a key challenge for constructing membrane-free desalination batteries. Herein, p-type N,N'-diphenyl-5,10-dihydrophenazine (PN)-derived polymer was introduced as the anion-selective electrode for desalination application. Leveraging the structural stability of PN active centers and the rigid framework nature of a 3D covalent organic framework (COF), the PN-derived 3D COF (3D-PN COF) exhibits good thermal stability and antidissolution property in acid/alkali solutions. Therefore, its derived electrode presents a high electrochemical stability under overdischarging conditions, as well as in pollutant-containing solutions. Coupled with a cation-selective Prussian blue analogue (PBA) electrode, this anion-selective 3D-PN COF enables a stable membrane-free desalination battery. Owing to the fixed redox potential of the 3D-PN COF and PBA electrode (both around 0.4 V vs Ag/AgCl), the oxygen reduction reaction (ORR) is restricted, which would cause desalination decay and the Faradaic rectification effect. This study not only demonstrates that p-type PN is a promising stable anion-selective redox center for desalination application but also verifies that the suitable redox potential of faradaic electrodes can suppress ORR without the help of a cation-exchange membrane to block dissolved oxygen from the electrode.