Argumentation has become one of the important fields of artificial intelligence. This paper proposes a dual-neighborhood tabu search (DNTS) method specifically designed to find a single stable extension in abstract argumentation frameworks. The proposed algorithm implements an improved dual-neighborhood strategy incorporating a fast neighborhood evaluation method. In addition, by introducing techniques such as tabu and perturbation, this algorithm is able to jump out of the local optimum, which significantly improves the performance of the algorithm. In order to evaluate the effectiveness of the method, the performance of the algorithm on more than 300 randomly generated benchmark datasets was studied and compared with the algorithm in the literature. In the experiment, DNTS outperforms the other method regarding time consumption in more than 50 instances and surpasses the other meta-heuristic method in the number of solved cases. Further analysis shows that the initialization method, the tabu strategy, and the perturbation technique help guarantee the efficiency of the proposed DNTS.