In order to study the evolution law of the fluctuation range of single variable time series, this article chose closing price in the afternoon of London Gold from January 1, 2002 to February 28, 2014 as the sample data, in refer to the method of statistical physics research. Using Parkinson's definition about fluctuation range, it defines the calculation method of single variable fluctuation range, and uses coarse-grained method to transform price fluctuation range into symbolic sequences consisted of three characters $\{H,M,L\}$. The nodes of the fluctuation range complex network are 5-symbol strings in the form of data window linked in the network's topology by sliding sequence. The single variable fluctuation range complex network is composed of 149 models and the link edges between them. The former 32 nodes account for 79\% of the strength degree distribution. It does not show a good correlation between weighted clustering coefficient and point of strength. There are 10 small clusters that contain 8 points and above it in the network. The average shortest path length of network is 6.561, which means the price fluctuation range has periodicity. Some points that have higher degree have weaker betweenness centrality, however, some other points that have lower degree have an important role in the route of the network. In summary, the paper used the complex network theory to analyze the statistics, variation and evolution regularity of single variable time series fluctuation range mode. The result shows that the single variable time series fluctuation range has the characteristic of power-law,clustering and periodicity, and its fluctuation range models mainly apply a handful of models to transfer and evolve. The research results in this paper can not only provide methods for different types of single variable time series fluctuation range research, but also provide ideas for multiple variables fluctuation range and its linkage variation rule research.