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Understanding of market efficiency is the cornerstone of market analysis. Oil market efficiency test can not only provide the theoretical foundation for oil price forecast but offer evidence of comparing the information efficiency of different markets. The generalized spectrum method is applied on the daily data from January 2001 to July 2008 to test the weak form efficiency of main crude oil markets in the world. Allowing for the stylized facts of high frequency data, this method can capture linear and nonlinear serial dependence while being robust to unknown form of conditional heteroskedasticity and checking all the lags. The results indicate that WTI of US and Brent of Europe have reached weak form efficiency; however, OPEC's and China's oil markets do not. The main cause is analyzed from the angles of market trading systems and the structure of market participants.