The extraction of weak acoustic signals under strong background noise is of great significance in the applications of target identification and localization. In this paper, the pulse signal with high randomness is set as the weak signal sound source, random noise and sine sound are used as the background noise. Under the condition of a signal-to-noise ratio of −20 dB, combined with blind source separation and neural network methods, the collected observation signals are subjected to weak sound signal separation and recognition research. The optimization method of centralization and scaling processing is used to eliminate the unfavorable influence of the uncertainty of the separated signal amplitude caused by the blind source separation method on the pattern recognition. The recognition result is verified by the combination of “weak impulse acoustic signal” and “random noise signal,” and the output vector (0.99 0.01 0.01) approaches (1 0 0), which is recognized as impulse acoustic signal. By combining blind source separation and neural network methods, the separation and identification of weak pulse signals under the condition of a signal-to-noise ratio of −20 dB can be achieved.