The convergence process and the advantages involved for less developed and developing countries, especially those located in the MENA region is of a great importance in economic studies. Through expanding regional co-operations and playing a wider role in the economies of the member states, it can prepare a suitable ground for growing regional markets and positive international economic reactions and finally can result into total development of the region. This article, using time series model is aiming at testing the convergence hypothesis in MENA region (15 countries) during 1980-2008. For analyzing time series model, we used Augmented Dicky Fuller test, Zivot & Andrews (with the endogenous time break) unit root test, Im, Pesaran & Shin and also Levin, Lin & Chu unit root panel data tests. The results of time series model with ADF and ZA tests show that there are two groups of convergence among the selected MENA countries. The first one is those countries which are converging from the low per capita income up to the average per capita income of the selected countries. The second one is the countries which are converging from the high per capita income down to the average of the region. The rest have diverged from the average per capita income during the period. According to Im, Pesaran & Shin and also Levin, Lin & Chu unit root tests, the convergence hypothesis of per capita income to average, is accepted for the whole sample. Altogether, the selected countries are minimizing the gap between their per capita income and the average per capita income of the region.