The invention relates to a fuel gas-hydrogen co-production process. The process adopts a two-section or three-section methanation furnace, fresh gas is preheated and hydrolyzed and is then mixed with compressor outlet gas, the mixed gas passes through a second reaction outlet heat exchanger and a first reaction inlet heat exchanger, and then enters a first reactor; the outlet gas undergoes treatment by a steam superheater, a first reaction inlet heat exchanger and a vapor generator, then the gas falls into two streams, one stream is mixed with fresh gas and then the mixed gas enters a second reaction outlet heat exchanger, and the other stream enters a second reactor, the second reaction gas undergoes treatment by a second reaction outlet heat exchanger, a fresh gas preheater, a boiler water heat preheater 2, a boiler water heat preheater 3, boiler water heat preheater 1 and a liquid separation tank 1, thus obtaining hydrogen-rich and methane-rich fuel gas. The boiler water heat preheater 3 outlet gas also can enter a third reactor through a liquid separation tank 2 and a third reaction inlet heat exchanger, and the third reaction gas undergoes treatment by a boiler water heat preheater 4, a third reaction inlet heat exchanger, the boiler water heat preheater 1 and the liquid separation tank 1, thus obtaining hydrogen-rich and methane-rich fuel gas. The method provided by the invention has the advantages of simple technological process, small investment and land occupation, and flexible and convenient operation, solves the fuel supply and the hydrogen balance problems of a whole plant, and has good economic benefits.