The price of crude oil is fluctuating. Researchers focus on the fluctuation of crude oil prices or relationship between crude oil futures and spot prices. However, the relationship also presents fluctuation which draws our attention. This paper designed a complex network approach for examining the dynamics of the co-movement between crude oil futures and spot prices. We defined the co-movement modes by a coarse-graining procedure and analyzed the transformation characteristics between the modes by weighted complex network models and evolutionary models. We analyzed the parameters of these models by using the West Texas Intermediate crude oil future prices and the Daqing (China) crude oil spot prices from November 25, 2002 to March 22, 2011 as sample data. The results indicate that the co-movement modes of the crude oil futures and spot prices are clustered around a few critical modes during the evolution. The co-movement of the crude oil prices has the characteristic of grouping, and the conversion of the co-movement modes requires an average of 5-7 days. There are some important transitional phases in the evolution of prices, and the results validate the current trend of rising oil prices. This research may provide information for the oil price decision-making process, and more importantly, provides a new approach for examining the co-movement between variables. (C) 2014 Elsevier Ltd. All rights reserved.