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Supplier selection is one of the most critical decisions in a supply chain. While it can contribute to the supply good suppliers, supply chain's overall incorrect selection can drive the whole chain into disarray. The back-propagation algorithm(BP) is a well-known method of training a multilayer feed-forward artificial neural networks(FFANNS). Although the algorithm is successful, it has some disadvantages. Because of adopting the gradient method by BP neural network, the problems including slowly learning convergent velocity and easily converging to local minimum can not be avoided. In addition, the selection of learning factor and inertial factor affects the convergence of BP neural network, which are usually determined by experiences. Therefore the effective application of BP neural network is limited. In this paper a new method in BP algorithm to avoid local minimum was proposed by means of adding gradually training data and hidden units. In addition, the paper also proposed a new model of controllable feed-forward neural network for supplier selection.