Emotion-cause pair extraction (ECPE), an emerging task in sentiment analysis, aims at extracting pairs of emotions and their corresponding causes in documents. This is a more challenging problem than emotion cause extraction (ECE), since it requires no emotion signals which are demonstrated as an important role in the ECE task. Existing work follows a two-stage pipeline which identifies emotions and causes at the first step and pairs them at the second step. However, error propagation across steps and pair combining without contextual information limits the effectiveness. Therefore, we propose a Dual-Questioning Attention Network to alleviate these limitations. Specifically, we question candidate emotions and causes to the context independently through attention networks for a contextual and semantical answer. Also, we explore how weighted loss functions in controlling error propagation between steps. Empirical results show that our method performs better than baselines in terms of multiple evaluation metrics. The source code can be obtained at https://github.com/QixuanSun/DQAN.