This paper describes how to efficiently solve a robust optimal control problem using recently developed primal-dual interior-point methods. One potential application is model predictive control. The optimization problem considered consists of a worst case quadratic performance criterion over a finite set of linear discrete-time models subject to inequality constraints on the states and control signals. The scheme has been prototyped in Matlab, To give a rough idea of the efficiencies obtained, it is possible to solve problems with more than 10 000 primal variables and 40 000 constraints on a workstation. The key to the efficient implementation is an iterative solver in conjunction with a Riccati-recursion invertible pre-conditioner for computing the search directions.