Convergence hypothesis is one of the results of neoclassical growth model, which has been examined recently. This hypothesis has two forms of absolute and conditional Beta-convergence and implies that regions with lower per capita output have higher per capita growth rates. Since there is no data for regional GDP in Iran, there has been n study to test convergence hypothesis in Iran. Our main contribution in this paper is testing convergence by using the data of demand deposits of Iran’s provinces and examining convergence in per capita demand deposits on the base of endogenous demand deposits creation theory in real business cycles approach. Our empirical results have provided some support for Beta-convergence in Iran’s regional growth when OLS is used. But our results do not support Sigma-convergence or decrease in regional inequality.