The task of deducing the causal network from time series data and identifying relationships among multiple series is increasingly vital across various sectors such as industry, medicine, and finance. Despite numerous algorithms being proposed for this purpose, the majority are predicated on the stationarity assumption. However, in disciplines like climatology and neuroscience, time series often exhibit non-stationarity, characterized by a data distribution that shifts over time. In this paper, we introduce an innovative algorithm designed to discern causal relationships from non-stationary time series. Our approach unfolds in three key steps: Initially, we harness the concept of copula entropy to estimate the conditional transfer entropy, offering a streamlined method for non-parametric conditional independence testing. Subsequently, we introduce the time index, which influences other variables at specific time lags, and by integrating the conditional transfer entropy, we execute the independence tests. This leads us to propose the CE-CDN (Copula Entropy-based Causal Discovery from Non-stationary time series), a two-stage algorithm tailored for learning the causal network and identifying change modules. Finally, through comparative analysis with existing algorithms, our experimental findings indicate that CE-CDN not only excels in managing non-stationary time series but also boasts commendable time efficiency.