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Finding the active sites of suitable metal oxides is a key prerequisite for detecting CH$$_4$$ 4 . The purpose of the paper is to investigate the adsorption of CH$$_4$$ 4 on intrinsic and oxygen-vacancies CuO (111) and (110) surfaces using density functional theory calculations. The results show that CH$$_4$$ 4 has a strong adsorption energy of −0.370 to 0.391 eV at all site on the CuO (110) surface. The adsorption capacity of CH$$_4$$ 4 on CuO (111) surface is weak, ranging from −0.156 to −0.325 eV. In the surface containing oxygen vacancies, the adsorption capacity of CuO surface to CH$$_4$$ 4 is significantly stronger than that of intrinsic CuO surface. The results indicate that CuO (110) has strong adsorption and charge transfer capacity for CH$$_4$$ 4 , which may provide experimental guidance.