Methane activation is one of the biggest challenges for chemical conversion of hydrocarbons and fundamental science. We systematically screen $d$-block transition metal elements as potential candidates of single-atom catalysts (SACs) for methane dissociation. The adsorption of methane on free metal atoms strongly depends on the number of $d$ electrons of SAC, where the maximum binding energy is formed with the Ni group (electronic configuration ${d}^{8}{s}^{2}$ or ${d}^{9}{s}^{1})$. Interestingly, the magnetic moment of the SACs decreases by $2{\ensuremath{\mu}}_{\mathrm{B}}$ for strong interactions, suggesting that the methane-metal bond forms a spin singlet state involving two electrons of opposite spins. To examine the effect of substrates, the screened transition metals, Ni, Rh, and Pt are further put onto prototype metal oxide surfaces. The substrate dramatically modifies the discrete energy levels of a single metal and its catalytic properties. Single Ni atoms supported on an O-terminated $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{A}{\mathrm{l}}_{2}{\mathrm{O}}_{3}(0001)$ surface $(\mathrm{N}{\mathrm{i}}_{1}/\mathrm{A}{\mathrm{l}}_{2}{\mathrm{O}}_{3})$ show superior catalytic properties, with a low activation barrier of 0.4 eV (0.11 eV after zero-point energy correction) for the C-H bond dissociation and simultaneously an extreme stability with a high binding energy of $\ensuremath{\sim}9.39\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$ for the Ni anchor. This work identifies $\mathrm{N}{\mathrm{i}}_{1}/\mathrm{A}{\mathrm{l}}_{2}{\mathrm{O}}_{3}$ catalyst as an optimal SAC and offers new atomistic insights into the mechanism of methane activation on SACs.