A new acoustic leak detection system for sodium-cooled reactor steam generators using a delay-andsum beamformer is proposed. The major advantage of the delay-and-sum beamformer is that it could provide information on the acoustic source direction. An acoustic source of a sodium-water reaction is supposed to be localized, while the background noise of the steam generator operation is uniformly distributed in the steam generator tube region. Therefore, the delay-and-sum beamformer could distinguish the acoustic source of the sodium-water reaction from the steam generator background noise. In this paper, results of numerical analyses are provided to show the fundamental feasibility of the new method.