Abstract: Multi-turn response selection is a task designed for developing dialogue agents. The performance on this task has a remarkable improvement with pre-trained language models. However, these models simply concatenate the turns in dialogue history as the input and largely ignore the dependencies between the turns. In this paper, we propose a dialogue extraction algorithm to transform a dialogue history into threads based on their dependency relations. Each thread can be regarded as a self-contained sub-dialogue. We also propose Thread-Encoder model to encode threads and candidates into compact representations by pre-trained Transformers and finally get the matching score through an attention layer. The experiments show that dependency relations are helpful for dialogue context understanding, and our model outperforms the state-of-the-art baselines on both DSTC7 and DSTC8*, with competitive results on UbuntuV2.