Modeling the time series complex network provides a new perspective for analyzing the time series. Some classical algorithms neglect the unidirectionality of the time and the difference in correlation between primitives. While the symbolized time series network can construct the network on a controlled scale and can construct the weighted directed network which is closer to reality. Combined with the seasonal-trend-loess method and the symbolized transformation of the periodic time series, a time series network construction method is proposed. Both the state of a single data value and the long-term trend of the time series are considered in our symbolized time series network. The symbolic modes are used as nodes, and the edges are defined according to the adjacent transformation relationship between nodes. The direction and the weight of the edges are determined according to the conversion direction and the conversion frequency. Then, the directed weighted network is established. The air passenger throughput time series and the Internet traffic time series are used as the experimental data respectively. The topological features of these two time series networks are obviously different. Furthermore, to mine the essential laws of time series data, the empirical analysis of the time series of mobile communication voices is carried out. Our work enriches the research results of time series networks.