β-NaFeO2 structure is an orthorhombic wurtzite-derived structure, of which the structural relationship with wurtzite structure is similar to that of the chalcopyrite sturcture with zincblende structure. β-LiGaO2, β-AgGaO2 and β-AgAlO2 are known as materials possessing the β-NaFeO2 structure; however, studies on the wurtzite-derived ternary oxide semiconductors are quite limited. Recently, we demonstrated the band gap engineering of zinc oxide by alloying with wurtzite-type β-AgGaO2, and the band gap of ZnO was reduced to 2.55 eV by this alloying. Very recently, a new wurtzite-type ternary compound, β-CuGaO2, was found out. Its energy band gap was 1.47 eV, and it exhibited p-type conduction. The first principle calculation indicated that β-CuGaO2 is a direct semiconductor; therefore it is suitable to use in optoelectronic devices. Taking the 1.47 eV of the band gap and p-type electronic conduction into account, β- CuGaO2 is a promising material for the thin film solar cell absorber. These new ternary oxide semiconductors possessing wurtzite-derived structure expanded the energy region that the oxide semiconductors cover into visible and near-infrared region.