In this paper we propose a new learning hyper-heuristic that is composed of a simple selection mechanism based on a learning automaton and a new acceptance mechanism, i.e. the Iteration Limited Threshold Accepting criterion. This hyper-heuristic is applied to the challenging Traveling Tournament Problem. We show that the new hyper-heuristic method, even with a small number of low-level heuristics, consistently outperforms another hyper-heuristic without any learning device. Moreover, the learning hyper-heuristic method, although very general, generates high-quality solutions for the tested Traveling Tournament Problem benchmarks.