The robust output regulation problem for a class of invertible nonlinear MIMO systems is addressed in this paper. Under a mild assumption on the high-frequency gain matrix and strongly minimum-phase assumption, a robust regulator is proposed with the combination of nonlinear internal model and a new extended high-gain observer. More explicitly, the robust output regulation is achieved by employing a novel extended high-gain observer-based stabilizer such that the regulated system, augmented with the nonlinear internal model, is asymptotically stabilized. The novelty of this approach consists in the use of an extended observer to estimate, under mild assumptions, all unmeasured terms. (C) 2017 Elsevier Ltd. All rights reserved.