According to the fluctuation series of the conventional gasoline spot prices (CGSP) in New York Harbor (NYH) and U.S. Gulf Coast (GC), this paper defines the fluctuation modes by the coarse-grained method based on the CGSP series in the two harbors. The fluctuation series are converted into the characters by means of the sliding window, where five symbol series is used as a fluctuation mode, one day was used as a step to slide in the data window, and the conventional gasoline spot prices fluctuation network (CGSPFN) is constructed in the two harbors. Then the evolutionary rule of the new nodes in the CGSPFN is analyzed, such as the strength and distribution, average shortest paths, conversion cycle, betweenness, and clustering coefficient of the nodes are calculated in different periods. The result indicates that the cumulative time of the new nodes which appeared in the CGSPFN is not random but presents a high linear growth trend, which reveals the linear features of the cumulative time of abnormal points when the gasoline price fluctuation appears. The betweenness and clustering coefficient shows that the nodes with the larger strength have smaller betweenness and clustering coefficients, the nodes with the larger betweenness have smaller strength and clustering coefficients, and the nodes with the larger clustering coefficients have smaller betweenness and strength. Meanwhile, the gasoline prices are in a transitional period when the larger indicators appear and have a rising trend, and identifying the transitional period will help the decision maker to grasp the regularity of the changes of the gasoline prices.