The entire process of Bosnia and Herzegovina's path to European integration so far, is mostly limited to the problems of achieving political consensus, neglecting the essence and purpose of the integration process, which is primarily reflected in achieving the real convergence of Bosnia and Herzegovina towards the EU. The absence of real convergence, and adequate preparation in terms of competitiveness of the economy of Bosnia and Herzegovina for the EU membership, can cause negative effects of integration.Considering that there has not yet been written any paper that questions the lack of real convergence, primarily GDP p.c., and that a complete analysis of economic criteria is reduced to the Progress Reports of Bosnia and Herzegovina towards the EU, which summarize the fulfillment of the economic criteria of Bosnia and Herzegovina for the EU membership without concrete suggestions for improvement, this paper analyzes the real convergence of Bosnia and Herzegovina towards the European Union, observed through the income level p.c., prices and productivity of the labor force.The analysis showed that there is a sigma convergence of Bosnia and Herzegovina towards the EU in the movement of GDP p.c., which is reflected in the reduction of the coefficient of variation of the observed parameter in the period from 2000 to 2015 from 89.8% to 85.3%, which is a decrease in the coefficient of variation for 4 , 5 p.p. for 16 years.In the observed period there was an increase in the absolute GDP p.c. gap, which means that Bosnia and Herzegovina must increase the rate of economic growth in the coming period, in order to stop the relative decrease in the standard of living in relation to the EU.In addition, the analysis of sigma convergence has shown that there are sigma divergent trends in the movement of productivity and price level of Bosnia and Herzegovina in relation to productivity and price level at the EU level.It is expected that the price level in Bosnia and Herzegovina will increase in the coming period as a result of the activation of the Stabilization and Association Agreement and a higher degree of trade integration with the EU.