The invention discloses a production system for extracting crude helium from natural gas and co-producing liquefied natural gas. The production system comprises a first-stage helium extraction unit, a second-stage helium extraction unit, a third-stage helium extraction unit, a mixed refrigeration system and a nitrogen refrigeration system, wherein the first-stage helium extraction unit, the second-stage helium extraction unit and the third-stage helium extraction unit are connected through pipelines. The first-stage helium extraction unit comprises a heat exchanger I, an LNG storage tank, a rectifying tower I, and a condenser I and a reboiler I which are arranged at the tower top and the tower bottom of the rectifying tower I correspondingly. The second-stage helium extraction unit comprises a heat exchanger II, a rectifying tower II, and a condenser II and a reboiler II which are arranged at the tower top and the tower bottom of the rectifying tower II correspondingly. The third-stage helium extraction unit comprises a heat exchanger III, a rectifying tower III, and a condenser III and a reboiler III which are arranged at the tower top and the tower bottom of the rectifying tower III correspondingly. According to the production system, the technical scheme of mixed refrigerant circulating refrigeration and three-stage rectification helium extraction is adopted, helium is produced as a main product, a small part of liquefied natural gas and liquid nitrogen products are produced as byproducts, and the problems of high investment, high operation cost and the like in an existing helium extraction and liquefied natural gas co-production process can be effectively solved.