The combination of underwater acoustic processing and the Global Navigation Satellite System (GNSS) has achieved remarkable economic benefits in offshore operations. As the key technology of GNNS positioning, feature extraction of underwater acoustic signals is affected by the complex marine environment. To extract more effective information from underwater acoustic signals, we use four types of multi-scale entropies, including multi-scale sample entropy (MSE), multi-scale fuzzy entropy (MFE), multi-scale permutation entropy (MPE), and multi-scale dispersion entropy (MDE), to analyze and distinguish underwater acoustic signals. In this study, two groups of real-word underwater acoustic signal experiments were performed for feature extraction of ship-radiated noises (SRNs) and ambient noises (ANs). The results indicated that the performance of the MFE-based feature extraction method is superior to that of feature extraction methods based on the other three entropies under the same number of features, and the highest average recognition rate (ARR) of the MFE-based feature extraction method for SRNs reaches 100% when the number of features is 3.