In this paper, a robust optimization framework is developed to train shallow neural networks based on reachability analysis of neural networks. To characterize noises of input data, the input training data is disturbed in the description of interval sets. Interval-based reachability analysis is then performed for the hidden layer. With the reachability analysis results, a robust optimization training method is developed in the framework of robust least-square problems. Then, the developed robust least-square problem is relaxed to a semi-definite programming problem. It has been shown that the developed robust learning method can provide better robustness against perturbations at the price of loss of training accuracy to some extent. At last, the proposed method is evaluated on a robot arm model learning example.