This paper considers the stability problem of a class of positive coupled differential-difference equations with unbounded time-varying delays. A new method, which is based on upper bounding of the state vector by a decreasing function, is presented to analyze the stability of the system. Different from the existing methods, our method does not use the usual Lyapunov-Krasovskii functional method or the comparison method based on positive systems with constant delays. A new criterion is derived which ensures asymptotic stability of the system with unbounded time-varying delays. A numerical example with simulation results is given to illustrate the stability criterion. (C) 2018 Elsevier Ltd. All rights reserved.