In this paper, income per capita convergence hypothesis is tested in selected OIC countries. For this purpose, we use the time series model and univariate KPSS stationary test with multiple structural breaks (Carrion-i-Silvestre et al. (2005)) over the period 1950-2008. The results show that most OIC countries could not catch up toward USA. Although because of some positive term of trade shocks, they experienced catching up process in some sub- periods, they did not have appropriate infrastructure as, they could not use these opportunities and escape lag deadlock.