Initial oxidation of methane (CH4) is essential for subsequent oxidation reactions on anode surfaces of solid oxide fuel cells (SOFCs). Here first principle method was employed to investigate the initial oxidation mechanism of CH4 on Pd doped LaCo0.2Fe0.8O3-δ (LCF) anode. Results show that Pd-doping decreases formation energies of surface oxygen vacancy. The adsorption ability of CH4 molecules is also improved on perfect LCF surface by Pd-doping. Dissociation barriers of CH4 on LCF surfaces are greatly decreased with min value of 1.14 eV by Pd-doping and surface oxygen vacancy compared to those on perfect and defective LCF surfaces (min values of 1.76 and 1.34 eV, respectively). Results of Bader charges and bond lengths of CH4 (or CH3) and OH show that the initial oxidation of CH4 molecules is namely the oxidation of dissociated H atoms from CH4 molecules. And higher valences of surface metal atoms interacted with CH4 molecules mean the lower dissociation barriers of CH4 molecules.