Heteroscedasticity of time series is an important issue addressed in relation to the nonlinearity and complexity of time series. Previous studies have focused on time series heteroscedasticity during a long-term period but have rarely analyzed it from a nonlinear dynamic perspective. This paper proposes a new model for converting a time series into a complex network. Our proposed model can examine not only the heteroscedasticity of a short-term series but also the dynamic evolution process of this heteroscedasticity. Using four typical crude oil time series as sample data, we construct four networks. A network node denotes the types of fluctuation patterns corresponding to the symbolization of the heteroscedastic features of a short-term fluctuation series based on the autoregressive generalized autoregressive conditional heteroscedasticity model, and a weighted edge represents the evolution direction and frequency between two patterns. Our findings show that the choice of the length of a short-term period depends on the diversity of these patterns. The identification of the nodes with greater out-strength or greater betweenness centrality can help us to understand the different roles of fluctuation patterns in the evolution process. We propose a method for predicting the most probable target nodes from a source node. The analysis of clustering effects can help in detecting the fluctuation patterns between different clusters. This paper investigates the evolution dynamic mechanism of the heteroscedastic features of a short-term time series, which can help researchers and investors deeply understand the dynamic process of time series.