An anti-noise interrogation technique for ultra-weak fiber Bragg grating (UWFBG)-based distributed acoustic sensing (DAS) systems is proposed and demonstrated using double-pulse-based time-domain adaptive delay interference. This technique breaks the limitation that the optical path difference (OPD) between the two arms of the interferometer should be completely matched with the entire OPD between the adjacent gratings in the traditional single-pulse system. The length of the delay fiber in the interferometer can be reduced, and the double-pulse interval can adapt flexibly to the UWFBG array with different grating spacing. The acoustic signal is restored accurately when the grating spacing is 15 m or 20 m by the time-domain adjustable delay interference. Moreover, the noise induced by the interferometer can be suppressed significantly as compared to using a single pulse, and above 8-dB signal-to-noise ratio (SNR) enhancement can be obtained without any extra optical devices when the noise frequency and the vibration acceleration are below 100 Hz and 0.1 m/s2, respectively.