In this paper, a novel robust regression model is proposed. The proposed robust regression model is called functional link least square (FLLS). The idea of the proposed FLLS model arises from the functional link artificial neural network (FLANN). The FLANN model can be established by using the Error Back propagation algorithm. However, the performance of the FLANN model is limited. Different from the FLANN model, the proposed FLLS model can achieve an optimal regression model by using the least square algorithm. The proposed FLLS model has some salient features: first, the algorithm of FLLS is extremely fast; secondly, the training errors of the FLLS model can be nearly minimized to be zero; third, the testing performance of FLLS model is robust. In order to evaluate the performance of the proposed regression model, case studies of modeling two complex chemical processes are provided. Two more models of the FLANN and the partial least square (PLSR) are also developed for comparisons. Results illustrated that the proposed FLLS regression model could significantly improve the testing performance. (C) 2016 Elsevier Ltd. All rights reserved.