The fast, tailored solution of linear, predictive control problems is important, yet challenging. We present an algorithm based on the fast gradient method and the method of multipliers for model predictive control of linear, discrete-time, time-invariant, systems with box constraints. The algorithm uses the augmented Lagrangian method to handle equality constraints, so it can takes advantage of the sparsity of the problem. We present different schemes to update the multipliers. An example illustrates the performance of the algorithm, which is competitive with other tailored solution methods.