This paper studies the problem of convex hull constraint in conventional empirical likelihood. Specifically, in the framework of regression, a balanced augmented empirical likelihood (BAEL)procedure through adding two synthetic data points is proposed. It can be used to resolve the under-coverage issue, especially in small-sample or high-dimension setting. Furthermore, some asymptotic properties for proposed BAEL ratio statistic are established under mild conditions. The proposed approach performs robust to different random errors by choosing a robust loss function. Extensive simulation studies and a real example are carried out to support our results.