This paper is makes an analysis of the process of convergence of income between the municipalities of the Minas Gerais (Brazil) in the period of 1980 to 2005, trying to identify the existence of clubs of convergence using a model threshold. Results indicated for the formation of four clubs of convergence, among them shows a process of convergence between the all clubs. Human capital proved to be significant in explaining the process of growth of the intermediate groups of municipalities richer. The results also indicated that the physical capital was significantly negative for explaining the process of economic growth of most rich clubs of convergence, demonstrating in this way, a negative role for public investment undertaken in the districts of the region.