The present invention relates to the technical field of chlorine-alkali industry, and specifically provides a three-electrode system-based two-step chlorine-alkali electrolytic method and device adopting dual electrolytic cells. The device of the present invention comprises two independent electrolytic cells (cell A and cell B), a hydrogen evolution catalytic electrode, a chlorine evolution catalytic electrode, and a sodium storage electrode capable of reversibly storing sodium ions. According to the method of the present invention, a process of electrolyzing a salt solution or seawater is divided into a step of producing hydrogen/sodium hydroxide and a step of producing chlorine, the two steps being completed in the two electrolytic cells (cell A and cell B) respectively. The electrolytic process in the electrolytic cell A and the electrolytic process in the electrolytic cell B are alternately carried out in a circulating mode. According to the present invention, a step of simultaneously producing hydrogen/sodium hydroxide and chlorine during conventional electrolysis of a salt solution or seawater is effectively divided, so that the step of producing hydrogen/sodium hydroxide and the step of producing chlorine are completed in different electrolytic cells respectively. Moreover, the desalination of the salt solution or seawater is realized; the costs of the chlorine-alkali industry are further reduced, the safety is greatly improved, the purity of the generated sodium hydroxide is effectively guaranteed, and moreover, the desalination of the salt solution or seawater is realized.