The obnoxious p-median problem consists of selecting p locations, considered facilities, in a way that the sum of the distances from each nonfacility location, called customers, to its nearest facility is maximized. This is an urn:x-wiley:09696016:media:itor12510:itor12510-math-0001-hard problem that can be formulated as an integer linear program. In this paper, we propose the application of a variable neighborhood search (VNS) method to effectively tackle this problem. First, we develop new and fast local search procedures to be integrated into the basic VNS methodology. Then, some parameters of the algorithm are tuned in order to improve its performance. The best VNS variant is parallelized and compared with the best previous methods, namely branch and cut, tabu search, and GRASP over a wide set of instances. Experimental results show that the proposed VNS outperforms previous methods in the state of the art. This fact is finally confirmed by conducting nonparametric statistical tests.