Time-domain beamforming is more suitable for blast wave transient signal than frequency-domain beamformer because wideband spectrum of noise makes the beamforming image less clear. To avoid the gust effects and enable the location of blast source accurately, this article proposes a new 1-D far-field delay-and-sum (DAS) beamforming method with an attenuate exponential function model for wireless overpressure transient signal. In addition, we design wireless overpressure peak and root-mean-square (rms) directional estimators to assess the performance of the proposed new DAS beamforming method. Furthermore, the effects of the wireless pressure sensor node (WPSN) spacing, the number of WPSNs, and sidelobe level brought from noise on the beamwidth are investigated in the two estimators. The proposed formula is verified by a uniformly spaced linear sensing array, and the results verify the feasibility of the proposed method in blast source localization. This article is conducted to provide new insight into blast source localization algorithm and further open a door for transient blast overpressure source localization scenarios in future.