The Three-Index Assignment Problem (AP3) is a famous NP-hard problem with wide applications. Since it’s intractable, many heuristics have been proposed to obtain near optimal solutions in reasonable time. In this paper, a new meta-heuristic was proposed for solving the AP3. Firstly, we introduced the conception of muscle (the union of optimal solutions) and proved that it is intractable to obtain the muscle under the assumption that P≠NP. Moreover, we showed that the whole muscle can be approximated by the union of local optimal solutions. Therefore, the Approximate Muscle guided Global Optimization (AMGO) is proposed to solve the AP3. AMGO employs a global optimization strategy to search in a search space reduced by the approximate muscle, which is constructed by a multi-restart scheme. During the global optimization procedure, the running time can be dramatically saved by detecting feasible solutions and extracting poor partial solutions. Extensive experimental results on the standard AP3 benchmark indicated that the new algorithm outperforms the state-of-the-art heuristics in terms of solution quality. Work of this paper not only provides a new meta-heuristic for NP-hard problems, but shows that global optimization can provide promising results in reasonable time, by restricting it to a fairly reduced search space.