NOVELTY - Low-carbon alcohol and natural gas are produced by when methane content in the coal base synthetic gas is more than 5%, purifying crude synthetic gas obtained by conversion of coal to remove sulfur to obtain purified synthetic gas whose carbon dioxide is less than 20 ppm and hydrogen sulfide is less than 0.1 ppm; collecting the sulfur product; and obtaining purified synthetic gas and methane after the synthetic gas is separated by pressure swing absorption, and directly using the methane as synthetic natural gas.    USE - Method for producing low-carbon alcohol and natural gas (claimed).    ADVANTAGE - The method has energy consumption, simple process, stable operation, and is easy to control.    DETAILED DESCRIPTION - Producing low-carbon alcohol and natural gas comprises:    (A) when methane content in the coal base synthetic gas is more than 5%, purifying crude synthetic gas obtained by conversion of coal to remove sulfur to obtain purified synthetic gas whose carbon dioxide (CO2) is less than 20 ppm and hydrogen sulfide (H2S) is less than 0.1 ppm; collecting the sulfur product; and obtaining purified synthetic gas and methane after the synthetic gas is separated by pressure swing absorption, and directly using the methane as synthetic natural gas;    (B) when the methane content in the coal base synthetic gas is less than 5%, purifying the crude synthetic gas obtained by conversion of coal to remove sulfur to obtain purified synthetic gas whose CO2 is less than 20 ppm and H2S is less than 0.1 ppm; and making the synthetic gas enter to alcohol-synthesizing reaction to obtaining sulfur product;    (C) making the purified synthetic gas synthesize to low-carbon alcohol under action of catalyst, and obtaining exhaust gas comprising methane (CH4), carbon monoxide (CO), hydrogen (H2), CO2, 1-5C hydrocarbon, and liquid product;    (D) separating the liquid product by hot trap to obtain wax and alcohol-water mixture containing oil; separating the alcohol-water mixture containing oil by cold strap to obtain alcohol-water mixture and oil; separating the alcohol-water mixture to obtaining water and alcohol; making the exhaust gas enter to pressure swing absorption, and separating out CH4 which is used as synthetic natural gas directly; making part of the exhaust gas removing CH4 enter to low-carbon alcohol synthesizing reaction; and making the other part enter to methanation reaction; and    (E) cooling and separating product to obtain lost of alcohol-water mixture and gas including 1-5C light hydrocarbon, H2, CO, and CO2; and making the gas mixture enter to CO2 removing unit, and synthesizing gas; or mixing with the coal base synthetic gas and part exhaust gas produced by the low-carbon alcohol, regulating hydrogen-carbon proportion, and making the product enter to the low-carbon alcohol synthesizing reaction.