First-principles calculations are performed to investigate the catalytic oxidation of methane by using N2O as an oxidizing agent over aluminum (Al)-doped Zn12O12 cluster and (Zn12O12)2 nanowire. The impact of Al impurity on the geometry, electronic structure, and surface reactivity of Zn12O12 and (Zn12O12)2 is thoroughly studied. Our study demonstrates that Al-doped ZnO systems have a better adsorption ability than the corresponding pristine counterparts. It is found that N2O molecule is initially decomposed on the Al site to provide the N2 molecule, and an Al-O intermediate which is an active species for the CH4 oxidation. The conversion of CH4 into CH3OH over AlZn11O12 and (AlZn11O12)2 requires an activation energy of 0.45 and 0.29eV, respectively, indicating it can be easily performed at normal temperatures. Besides, the overoxidation of methanol into formaldehyde cannot take place over the AlZn11O12 and (AlZn11O12)2, due to the high energy barrier needed to dissociate C-H bond of the CH3O intermediate. Dispersion-corrected density functional theory calculations were performed through GGA-PBE exchange-correlation functional combined with a numerical double-ζ plus polarization (DNP) basis set as implemented in DMol3. To include the relativistic effects of core electrons of Zn atoms, DFT-semicore pseudopotentials were adopted. The DFT + D scheme proposed by Grimme was used to involve weak dispersion interactions within the DFT calculations. The reaction energy paths were generated by the minimum energy path calculations using the NEB method.