In this paper, a new hybridization of a Myopic and Neighborhood approaches is proposed to solve large-size vertex p-median location problems. The effectiveness and efficiency of our approach are demonstrated empirically through an intensive computational experiment on large-size instances taken from TSPLib and BIRCH datasets, with the number of nodes varying from 734 to 9,976 for the former and from 9,600 to 20,000 nodes for the latter. The results show that the new approach, though relatively simple, yields better solutions compared to the ones in the literature. This demonstrates that a simpler approach that takes into account the advantages of other methods can lead to promising outcome and has the potential of being adopted in other combinatorial optimization problems.