The introduction of the Euro has drawn interested parties’ attention on the Euro/U.S. Dollar exchange rate market. In this research, three variance ratio tests: Lo-MacKinlay’s (1988) conventional variance ratio test, Chow-Denning’s (1993) simple multiple variance ratio test, and Wright’s (2000) non-parametric ranks and signs based variance ratio tests are adopted to test the random walk hypothesis (RWH) of the Euro/U.S. Dollar exchange rate market using the data from January 1999 to July 2008. All of three variance ratio tests’ results show that the RWH cannot be rejected. Therefore, the Euro/U.S. Dollar exchange rate market is regarded as weak-form efficient