NOVELTY - A double rare-earth element catalyst contains 0.5-10 wt.% rare earth metal oxide, 20-60 wt.% transition element oxide main active component, 10-50 wt.% composite carrier, and 2-20 wt.% water-repellent and heat stabilizing agent.    USE - Double rare-earth element catalyst for catalytic synthesis of methane and hydrogen and preparation of synthetic natural gas (all claimed).    ADVANTAGE - The catalyst has high strength, activity, and conversion rate, and simple preparation, is uniform and stable, and does not need high reactor for process.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are included for:    (1) preparation of double rare-earth element catalyst which involves dissolving transition metal element in nitric acid to obtain transition metal nitrate solution with 100-300 g/L transition element concentration, dissolving double rare-earth metal alloy solution with greater than or equal to 90% rare-earth metal content in nitric acid to obtain rare-earth element nitrate solution with 100-200 g/L rare-earth metal concentration, mixing prepared solutions in alkali liquid which is weakly alkaline in which volume ratio transition nitrate solution:rare-earth metal nitrate solution is 3-10:1, washing using desalted water, filtering, drying, mixing and kneading alumina and silicon oxide, adding water-repellent and heat-stabilizing agent, kneading to obtain composite carrier, mixing materials, grinding, granulating, calcining at 400-550 degrees C, tablet-forming, and performing hydrogen pre-reduction treatment at 400 degrees C for 70-85 hours in which catalyst has 0.18-2 mm particle diameter;    (2) application of double rare-earth element catalyst for catalytic synthesis of methane and hydrogen to obtain high concentrated carbon oxide which has 8-20% carbon oxide concentration; and    (3) application of double rare-earth element catalyst for preparing synthetic natural gas which involves performing continuous synthesis of catalyst and coke methane oven gas in 4 series of alkylation reactor and supplementing with carbon-water.    DESCRIPTION OF DRAWING(S) - The drawing shows a process flow diagram of methanation process. (Drawing includes non-English language text).