Extreme learning machine (ELM) has been well recognized as an effective learning algorithm with extremely fast learning speed and high generalization performance. However, to deal with the regression applications involving big data, the stability and accuracy of ELM shall be further enhanced. In this paper, a new hybrid machine learning method called robust AdaBoost.RT based ensemble ELM (RAE-ELM) for regression problems is proposed, which combined ELM with the novel robust AdaBoost.RT algorithm to achieve better approximation accuracy than using only single ELM network. The robust threshold for each weak learner will be adaptive according to the weak learner’s performance on the corresponding problem dataset. Therefore, RAE-ELM could output the final hypotheses in optimally weighted ensemble of weak learners. On the other hand, ELM is a quick learner with high regression performance, which makes it a good candidate of “weak” learners. We prove that the empirical error of the RAE-ELM is within a significantly superior bound. The experimental verification has shown that the proposed RAE-ELM outperforms other state-of-the-art algorithms on many real-world regression problems.