The purpose of this paper is to analyze whether the formation of an FTA will converge or diverge the income levels of its member countries. Although similar former studies predicted, to a certain degree, the possibility of economic convergence among FTA members, they failed to provide accurate research methods or reliable conclusions. Therefore, this study focuses on introducing the new concept of ‘accelerated convergence’ for the estimation of economic convergence to fully analyze the pure effects of an FTA on the income level convergence among its members. The empirical analysis from the cases of the creation and expansion of the EU and the formation of AFTA and ANZCER, proves that an FTA will certainly introduce an economic convergence effect on its members. This means that, in the pursuit of an FTA, it is desirable for Korea to establish an FTA with advanced countries, such as the U.S. or Japan, to maximize the benefits of economic convergence.