The paper tests the hypothesis that developing member states of the European Union converge to richer countries. On the basis of a Cobb-Douglas production function this study estimates beta convergence, and sigma convergence, utilising data from the 28 EU member countries. The results confirm the hypothesis and indicate that poor countries grow faster than rich economies in terms of per capita income and the convergence process for Malta is slower. This finding has important implications for transition EU member states, including that Malta needs to overcome several constraints in the transitional phase to increase the steady state level.