There have been much difficulties to construct an optimized neural network in complex nonlinear regression problems such as selecting the networks structure and avoiding overtraining problem generated by noise. In this paper, we propose a stepwise constructive method for neural networks using a flexible incremental algorithm. When the hidden nodes are added, the flexible incremental algorithm adaptively controls the number of hidden nodes by a validation dataset for minimizing the prediction residual error. Here, the ELM (Extreme Learning Machine) was used for fast training. The proposed neural network can be an universal approximator without user intervene in the training process, but also it has faster training and smaller number of hidden nodes. From the experimental results with various benchmark datasets, the proposed method shows better performance for real-world regression problems than previous methods.