The aim of this paper is to investigate whether Islamic banks have greater market power than conventional banks, as they might benefit from a captive client base. To measure market power, we compute Lerner indices for a sample of banks from 17 countries where Islamic and conventional banks coexist over the period 2000-2007. We also use the Rosse-Panzar model to measure the degree of competition for each type of banks. We find that Islamic banks do not have greater market power than conventional banks. We attribute the competitive behavior of Islamic banks to differences in norms and incentives.