With the widespread usage of video capture devices and social media videos, videos are dominating the multimedia landscape. There is an emerging need for video quality assessment (VQA) that forms the backbone of advanced video systems. Night-time videos play an important role in user capturing, hence being able to accurately assess their quality is critical. However, the characteristics of night-time videos differ from those of general in-capture videos; and VQA algorithms that have been developed for general-purpose videos cannot accurately assess the quality of night-time videos. Research is needed to gain a better understanding of how humans perceive the quality of night-time videos, and use this new understanding to develop reliable VQA algorithms. To this end, we construct a large-scale night-time VQA database, namely Mobile In-capture Night-time Database for Video Quality (MIND-VQ), containing 1181 nighttime videos, 435 subjects, and over 130000 opinion scores. We perform thorough analyses to reveal subjective quality assessment behaviors of night-time videos. Furthermore, we propose a new VQA model, namely Visibility-based Night-time Video Quality Assessment Network, VINIA. Spatial and temporal visibilityaware components are characterized to reflect properties of human perception of night-time VQA task. A series of experiments are conducted to compare our VINIA with other existing IQA/VQA algorithms using our new MIND-VQ database and other public VQA databases. Experimental results show that our subjective VQA database provides new insights and our new VINIA model achieves superior performance in accessing night-time video quality.