A new carbon-based mono-layer atomic crystal, phagraphene, was proposed recently, which has received increasing attention. We here consider variations of edge chemistry for a phagraphene nanoribbon, and also explore to expand its functional properties, some typical nonmetallic atoms are used as ribbon-edge terminations. With these edge chemistry, the bandgap of ribbons may be nearly unchanged, increased, or decreased as compared with the bare-edge ribbon, and even a quasi-metal or metal arises, presenting rich and flexibly tunable electronic st...