The objective of this study is to examine the nonlinear characteristics of the Euro exchange rate. Many nonlinear approaches have been applied in the finance field. Multifractal detrended fluctuation analysis (MF-DFA) is one of the popular methodologies employed to detect the nonlinear properties of a time series. The MF-DFA analysis is executed by removing the trend of a time series and abstracting its multifractality. This paper examines the features of the entire Euro exchange rate series and the sub-periods during the Global Financial Crisis and European Sovereign Debt Crisis. The overall pattern of the Euro exchange rate is determined. Further, the degrees of complexity during the two crisis periods are detected.