Monodoping with Mo, Cr, and N atoms, and codoping with Mo-N and Cr-N atom pairs, are utilized to adjust the band structure of NaNbO3 , so that NaNbO3 can effectively make use of visible light for the photocatalytic decomposition of water into hydrogen and oxygen, as determined by using the hybrid density functional. Codoping is energetically favorable compared with the corresponding monodoping, due to strong Coulombic interactions between the dopants and other atoms, and the effective band gap and stability for codoped systems increase with decreasing dopant concentration and the distance between dopants. The molybdenum, chromium, and nitrogen monodoped systems, as well as chromium-nitrogen codoped systems, are unsuitable for the photocatalytic decomposition of water by using visible light, because defects introduced by monodoping or the presence of unoccupied states above the Fermi level, which promotes electron-hole recombination processes, suppress their photocatalytic performance. The Mo-N codoped NaNbO3 sample is a promising photocatalyst for the decomposition of water by using visible light because Mo-N codoping can reduce the band gap to a suitable value with respect to the water redox level without introducing unoccupied states.