A training data selection method for multi-class data is proposed. This method can be used for multilayer neural networks (MLNN). The MLNN can be applied to pattern classification, signal process, and other problems that can be considered as the classification problem. The proposed data selection algorithm selects the important data to achieve a good classification performance. However, the training using the selected data converges slowly, so we also propose an acceleration method. The proposed training method adds the randomly selected data to the boundary data. The validity of the proposed methods is confirmed through the computer simulation.