According to the importance of oil prices on the economy, the main objective of the present study was to investigate the weak form efficiency hypothesis in main crude oil markets, OPEC, WTI and Brent. For this purpose, the two method of wavelets and fractional Brown motion and daily data of oil price for period 2003:1 - 2013:9 were used. The results showed that the OPEC basket price time series and Brent have long range dependence. This means that according to these results, the hypothesis that the weak form efficiency of Brent crude oil market and the OPEC basket price will reject, but evidence for rejecting the hypothesis was not for WTI crude oil. In addition to predictability, there is another consequence of long range dependence in a time series is a shock effect on oil prices, due to factors such as war or the international financial crisis, will remain so for a long time. Thus, consideration to this instance for determination public expenditures and investments by government, constitute the most important recommendations of this study.