We address the identification of direct causes in time series with multiple time lags, and propose a constraint-based window causal graph discovery method. A key advantage of our method is that the number of required conditional independence (CI) tests scales quadratically with the number of sub-series. The method first uses CI tests to find the minimum trek lag between two arbitrary sub-series, followed by designing an efficient CI testing strategy to identify the direct causes between them. We show that the method is both sound and complete under some graph constraints. We compare the proposed method with typical baselines on various datasets. Experimental results show that our method outperforms all the counterparts in both accuracy and running speed.