Methane (CH_4) is an important greenhouse gas that is 25 times that its CO_2 equivalent. There is low concentration (0.05% ~0.5%) CH_4 leakage in marine natural gas engine exhaust. It is difficult to capture and utilize low concentration CH_4 because of its stable chemical structure and high ignition temperature. Catalytic oxidation is the main method to remove low concentration CH_4 from tail gas. The noble metal palladium (Pd) is the best catalytic material for the complete oxidation of low concentration CH_4. In this paper, the main research progress of Pd-based catalysts is reviewed for their low-temperature activity, reliability and development cost. Firstly, the effects of Pd particle size and valence distribution, Pd dispersion state, type of support and strong metal-support interaction (SMSI) on methane oxidation activity are clarified; then, the mechanism of methane oxidation on the surface of Pd-based catalysts is summarized; in addition, the deactivation mechanisms of Pd-based catalysts, such as high temperature sintering, water poisoning and sulfur poisoning, are described in detail; finally, the main challenges and the future development of Pd-based catalysts for the complete oxidation of low concentration methane are summarized, and the strategies for improving the performance of Pd-based catalysts are proposed.