We describe a novel photocatalyst obtained by codoping GaN with CrO, according to a new "noncompensated" codoping concept based on first-principles calculations. The approach enables controllable narrowing of the GaN band gap with significantly enhanced carrier mobility and photocatalytic activity in the visible light region and thus offers immense potential for application in solar energy conversion, water splitting, and a variety of solar-assisted photocatalysis. Our calculations indicate that the formation energy for the cation doping is greatly reduced by noncompensated codoping with an anion. Although Cr doping alone can split the band gap with the formation of an intermediate band, the mobility is low due to carrier trapping by the localized states. The first-principles calculations also demonstrate that CrO codoping of GaN shifts the Fermi level into the conduction band resulting in high carrier density and mobility.