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3D surface moment invariants are a kind of integral invariants under translation, uniform scaling and rotation, and can be regarded as shape descriptors of 3D unclosed polygonal models. Few of the former literature used prior knowledge from the training set for supervised learning. In this paper, we illustrate how to select the training data and how to feed the feature vectors of the training models to back-propagation neural network for learning. Experimental result shows that the test models are sorted into the correct classes with high accuracy, including two-class classification and multi-class classification. Furthermore, we develop a novel method which uses weighted Manhattan distance to embed classification information into the traditional shape retrieval systems properly. It could determine and refine the retrieval results efficiently.