The three-dimensional (3-D) sound speed structure of the ocean is a fundamental environmental element in studying underwater sound propagation modeling and forecasting. The accurate classification of the sound speed fields (SSFs) provides a comprehensive understanding and analysis of the sound propagation pattern. To take advantage of the 3-D structure of the ocean SSFs, this paper presents a quick method based on tensor decomposition for classifying the ocean 3-D SSFs. Utilizing the WOA18 dataset, High Order Iterative Orthogonal (HOOI) decomposition of the 3-D SSFs is executed so as to accurately extract the characteristic information of the SSFs. The Fuzzy C-Means clustering (FCM) method is applied to classify the feature tensors, partitioning of regional categories in different seasons and revealing the typical SSFs structures. By combining the BELLHOP model with analysis of the characteristics of the first convergence zone of each category, it is concluded that there are six categories of SSFs in the Western Pacific Ocean. The SSFs across all categories are primarily latitudinally distributed, featuring distinct sound channel axes and surface sound speed variations.