In order to study the fluctuation of bivariate correlation which had time series characters, this paper selected International crude oil futures prices and Chinese Daqing crude oil spot prices as the sample data, using the method of statistical physics to study. The modes of fluctuation of correlation were defined by coarse graining process. Then three problems modes' statistics, law of variation and evolution mechanism were analyzed by complex network theory and analytical method. The results indicated that forms of modes showed that consecutive days of weak or strong positive correlation, and modes obeyed the power-law distribution. There were three kinds of sub-groups appearing in the network of fluctuation of bivariate correlation. These sub-groups were fluctuation of weak positive correlation, strong positive correlation and unrelated, and a core mode existed in each category of sub-groups. Transmission and evolution of fluctuation of bivariate correlation were a few modes. The fluctuation of bivariate correlation was transmitted and evolved by a few modes. The fluctuation had periodicity that the transmission among modes need average 8.74 days and a whole volatility cycle need about 18.55 days. These results not only can be the analyze method between two variables but also provides idea for researching a general law in different variables.