We propose a new algorithm for the solution of the robust multiple-load topology optimization problem. The algorithm can be applied to any type of problem, e.g., truss topology, variable thickness sheet or free material optimization. We assume that the given loads are uncertain and can be subject to small random perturbations. Furthermore, we define a rigorous measure of robustness of the given design with respect to these perturbations. To implement the algorithm, the users only need software to solve their standard multiple-load problem. Additionally, they have to solve a few small-dimensional eigenvalue problems. Numerical examples demonstrate the efficiency of our approach.