This paper proposes a dual fast gradient-projection method for solving quadratic programming problems that arise in model predictive control of linear systems subject to general polyhedral constraints on inputs and states. The proposed algorithm is well suited for embedded control applications in that: 1) it is extremely simple and easy to code; 2) the number of iterations to reach a given accuracy in terms of optimality and feasibility of the primal solution can be tightly estimated; and 3) the computational cost per iteration increases only linearly with the prediction horizon.