In recent years, interest in aquaculture acoustic signal has risen since the development of precision agriculture technology. Underwater acoustic signals are known to be noisy, especially as they are inevitably mixed with a large amount of environmental background noise, causing severe interference in the extraction of signal features and the revelation of internal laws. Furthermore, interference adds a considerable burden on the transmission, storage, and processing of data. A signal recognition curve (SRC) algorithm is proposed based on higher-order cumulants (HOC) and a recognition-sigmoid function for feature extraction of target signals. The signal data of interest can be accurately identified using the SRC. The analysis and verification of the algorithm are carried out in this study. The results show that when the SNR is greater than 7 dB, the SRC algorithm is effective, and the performance improvement is maximized when the SNR is 11 dB. Furthermore, the SRC algorithm has shown better flexibility and robustness in application.