The final paper is about analysis of banking system of Luxembourg, one of the Member States of European Union, from 2011 to 2015, more preciously it shows deeper analysis of segments of a particular part of the banking system in Luxemborg. Banking system of The Grand-Duchy of Luxembourg is analyzed within the European Economic Area, as Luxembourg is considered as a member of the area. This paper, besides the wide range of banking services, emphasizes the importance of ATMs, POS terminals, EFTPOS terminals and payment cards due to their role and contribution in the banking system of this country. The main aim of the paper is to show the development of financial system in Luxembourg. In the paper are used inductive and deductive methods, methods of analysis and synthesis, descriptive methods, generalization methods, comparative methods, classification methods and methods of proofing. The benefits of this research can be seen in a disclosure of a new knowledge of country's banking systems. In the paper are analyzed relationship between the number of population and number of payment cards, whether number of credit institutions depends on the number of inhabitants and the level of GDP, as well as connection of ATM network with the number of payment cards.