Direct methane conversion into value-added products becomes more important. Due to inertness of methane, cleaving the first C-H bond has been very difficult requiring high reaction temperature on the heterogeneous catalysts. Once the first C-H bond becomes activated, the remaining C-H bonds are successively dissociated on the metal surface, hindering the direct methane conversion into chemicals. Here, a single-atom catalyst of precious metals dispersed on $ZrO_2$ surface has been synthesized and used for selective activation of methane. The single-atomic nature was confirmed by extended X-ray fine structure analysis, electron microscopy images, and diffuse reflectance infrared Fourier transform spectroscopy. A model of the single-atom $Rh/ZrO_2$ catalyst was constructed by density functional theory calculations, and it was shown that $CH_3$ intermediates can be energetically stabilized on the single-atom catalyst. The direct conversion of methane into methanol was performed using $H_2O_2$ as an oxidant in the aqueous solution. Whereas Rh nanoparticles produced $CO_2$ only, the single-atom Rh catalyst produced methanol. Direct conversion of methane into ethane was performed in gas-phase reaction.