The invention relates to a fuel gas processing method for an FLNG (floating liquefied natural gas) oil-gas storage and offloading device. The method comprises the following steps: 1), multiple fuel gas sources are prepared; 2), a low-temperature compression system and a normal-temperature compression system are arranged, wherein the low-temperature compression system comprises a precooling device, a liquefying device, a throttle valve, an LNG storage tank and a low-temperature BOG (boil off gas) compressor, and the normal-temperature compression system comprises a precooling device, a liquefying device, a throttle valve, an LNG storage tank, three normal-temperature BOG compressors and three coolers; 3), the BOG obtained through high-pressure LNG throttling and flash evaporation, the BOG obtained through heat absorption and evaporation of the LNG storage tank and the BOG obtained through heat absorption and evaporation of an LPG (liquefied petroleum gas) storage tank are controlled to enter the low-temperature compression system, the fuel gas produced by condensate oil of a stabilizer and a small amount of fuel gas produced through deacidification are controlled to enter the normal-temperature compression system, a fuel gas low-temperature compression process and a fuel gas normal-temperature compression process are finished respectively; 4), technological process simulation software is adopted to calculate power consumption of each processing device and the total power consumption; 5), the processing process of the fuel gas sources is further optimized and analyzed. The fuel gas processing method can meet the operation requirement of the LFNG in a special maritime environment, and the operation safety and economy are improved.