The upgrading of landfill gas (LFG) to bio-methane is a feasible scheme to make full use of its energy and solve the environmental pollution problems caused by its emissions. In the process of LFG upgrading, deoxygen is an essential procedure. In order to develop highly efficient and low-cost catalysts for LFG deoxygen, a series of Cu/H-ZSM-5 zeolites with the content of copper (Cu) in the range of 0.95 wt%-10.48 wt% were prepared by incipient wetness impregnation method, and used in the removal of oxygen in simulated LFG. The results of deoxygen experiments showed that the Cu/H-ZSM-5 zeolite had an excellent catalytic activity comparable to noble-metal based catalysts. The light-off temperature of Cu(3.63)/H-ZSM-5 was as low as 321 °C under the experimental conditions with a gas hourly space velocity (GHSV) of feed gas (55 vol% methane, 1 vol% oxygen and 44 vol% carbon dioxide) at 68,790 h−1. According to the characterization results of the catalysts, it was supposed that the excellent catalytic deoxygen performance of the Cu/H-ZSM-5 zeolite might be mainly due to that it contains a variety of highly dispersed active Cu species, which could significantly reduce the activation energy barrier of methane. This work provides new insights into the development of low-cost high-performance LFG deoxygen catalysts in practical LFG upgrading engineering applications.