A failure diagnosis method and a failure diagnosis system of a dual purge system may determine whether a closed stuck failure or an opened stuck failure occurs in a line forming a dual purge system by measuring a pressure in a negative pressure formation device and comparing the corresponding pressure with a predetermined reference value when a purge valve of the dual purge system is in an opened or closed state, and may determine whether the failure occurs in components related to a secondary purge line in the dual purge system in which it is difficult to determine whether the failure occurs in a conventional failure diagnosis method of a single purge system in a simple method.