The predictive controls are one of the major control strategies in the process control. However, in general, an exact model of the controlled system is required in order to predict the system's outputs accurately. In this paper, we propose an adaptive predictive control using an adaptive output predictor with a simple structure for uncertain controlled systems. In the proposed method, the stability of the obtained adaptive predictive control system will be confirmed by setting a novel input constraint, "almost strictly positive real (ASPR) constraint". (C) 2015 Elsevier Ltd. All rights reserved.