Underwater pipelines are exposed to harsh environments, including high salinity, multi-modal vortex corrosion, and severe wave interference. Their safety is essential for the development and transportation of marine energy. Therefore, real-time safety monitoring of long-distance energy pipelines is of great strategic importance for ensuring the safety of life and property and energy security. With the rapid development of energy development, the corrosion and leakage mechanisms of natural gas pipelines, as well as their identification and early warning, have become the focus of attention. Optical fiber sensing technology has been applied to various energy safety monitoring fields. However, the mechanism of sound source fluctuations in pipeline leakage and the mutual coupling mechanism between distributed optical fiber sensing technology and leakage sound waves are not yet clear. This paper establishes a model based on sound wave propagation and leakage noise response, derives a quadratic fitting relationship between pipeline pressure fluctuations and leakage orifices and a relationship between leakage noise source standard deviation and orifices, and proposes a complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) permutation entropy underwater natural gas pipeline leakage signal recognition method based on distributed optical fiber acoustic sensing technology. The results of theoretical analysis are verified by experiments. It shows that the signal processing method of CEEMDAN permutation entropy is superior to traditional noise reduction methods, which can better preserve the features of the original signal; the radial basis function (RBF) neural network model can accurately identify four different leakage features with an accuracy of 88.15%, and its recognition stability and generalization ability are superior to convolutional neural network, backpropagation, and random forest. Therefore, the research results of this paper provide a new method for safety monitoring in the application of energy pipeline transportation engineering, and expand the potential application scenarios of distributed acoustic sensing sensor systems and RBF neural networks.