Grey wolf optimizer (GWO) is a recent swarm intelligence metaheuristic that mimics the leadership hierarchy of grey wolves. GWO was originally developed to address continuous optimization problems however, various versions of GWO algorithms are available in the literature that have been successfully applied to a wide range of problems. This work presents a modified version of the algorithm for solving the traveling salesman problem, a well-known NP-hard problem that is widely adopted in real-world applications. The performance of the proposed method has been tested over several TSP instances from TSPLIB and the result has been compared with other well-known meta-heuristics algorithms. The experimental findings showed that the proposed algorithm has promising performance and was able to overcome other algorithms in 55.56% of cases.