This article introduces a new method for identifying anchor damage faults in fiber composite submarine cables. The method combines the Volterra model of Variation Mode Decomposition (VMD) with singular value entropy to improve the accuracy of fault identification. First, the submarine cable vibration signal is decomposed into various Intrinsic Mode Functions (IMFs) using VMD. Then, a Volterra adaptive prediction model is established by reconstructing the phase space of each IMF, and the model parameters are used to form an initial feature vector matrix. Next, the feature vector matrix is subjected to singular value decomposition to extract the singular value entropy that reflects the fault characteristics of the submarine cable. Finally, singular value entropy is used as a feature value to input into the Support Vector Machine (SVM) for classification. Compared with Empirical Mode Decomposition (EMD) and Ensemble Empirical Mode Decomposition (EEMD), the proposed method achieves a higher fault identification accuracy and effectively identifies anchor damage faults in submarine cables. The results of this study demonstrate the feasibility and practicality of the proposed method.