Video-text retrieval is an emerging stream in both computer vision and natural language processing communities, which aims to find relevant videos given text queries. In this paper, we study the notoriously challenging task, i.e., Unsupervised Domain Adaptation Video-text Retrieval (UDAVR), wherein training and testing data come from different distributions. Previous works merely alleviate the domain shift, which however overlook the pairwise misalignment issue in target domain, i.e., there exist no semantic relationships between target videos and texts. To tackle this, we propose a novel method named Dual Alignment Domain Adaptation (DADA). Specifically, we first introduce the cross-modal semantic embedding to generate discriminative source features in a joint embedding space. Besides, we utilize the video and text domain adaptations to smoothly balance the minimization of the domain shifts. To tackle the pairwise misalignment in target domain, we introduce the Dual Alignment Consistency (DAC) to fully exploit the semantic information of both modalities in target domain. The proposed DAC adaptively aligns the video-text pairs which are more likely to be relevant in target domain, enabling that positive pairs are increasing progressively and the noisy ones will potentially be aligned in the later stages. To that end, our method can generate more truly aligned target pairs and ensure the discriminality of target features.Compared with the state-of-the-art methods, DADA achieves 20.18% and 18.61% relative improvements on R@1 under the setting of TGIF->MSRVTT and TGIF->MSVD respectively, demonstrating the superiority of our method.