Causality analysis, beyond "mere" correlations, has become increasingly important for scientific discoveries and policy decisions. Many of these real-world applications involve time series data. A key observation is that the causality between time series could vary significantly over time. For example, a rain could cause severe traffic jams during the rush hours, but has little impact on the traffic at midnight. However, previous studies mostly look at the whole time series when determining the causal relationship between them. Instead, we propose to detect the partial time intervals with causality. As it is time consuming to enumerate all time intervals and test causality for each interval, we further propose an efficient algorithm that can avoid unnecessary computations based on the bounds of F-test in the Granger causality test. We use both synthetic datasets and real datasets to demonstrate the efficiency of our pruning techniques and that our method can effectively discover interesting causal intervals in the time series data.