In this paper, we study the capacitated modular hub location problem. The problem belongs to the class of the single assignment hub location problems, where a terminal can be assigned to only one hub. In addition, the problem imposes capacity constraints, on both hubs and edges that connect them. The observed problem is directly related to the real problem. Namely, in air traffic, the number of flights between two cities directly determines the conditions of the capacity. In order to tackle the problem we propose a general variable neighborhood search (GVNS) based heuristic. We have performed exhaustive testing that led to the conclusion that the GVNS method gave superior results in comparison to the previous methods. This is especially reflected in the number of best solutions that were obtained in a much shorter time. Additionally, we applied statistical tests which showed that GVNS is undoubtedly superior with respect to the previously observed methods.