In this paper we propose a tube-based robust model predictive control scheme for fractional-order discretetime systems of the Grünwald-Letnikov type with state and input constraints. We first approximate the infinitedimensional fractional-order system by a finite-dimensional linear system and we show that the actual dynamics can be approximated arbitrarily tight. We use the approximate dynamics to design a tube-based model predictive controller which endows to the controlled closed-loop system robust stability properties.