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Mobile crowdsensing offers a new platform that recruits a suitable set of users to collectively complete an information collection/sensing task through users' equipped devices. As a special case, video crowdsensing is to collect different video segments of the same event that are taken separately by the built-in cameras of mobile devices, and then combine them into a complete video. Mobile crowdsensing has attracted considerable attention recently due to the rich information that can be provided by videos. However, because of the limited caching space, a suitable video replacement policy is necessary. In this paper, we propose a Budgeted Video replaCement policy in mobile Video crowdsensing (BVCV), which first determines a video segment's value according to its caching situation and natural attributes. Then, we formulate the video caching problem as a budgeted maximum coverage problem, which is a well-known NP-hard problem. Finally, we propose a practical greedy solution and also infer the approximate ratio, which could be regarded as the lower bound of BVCV to the optimal solution. Our experiments with the real mobility datasets (StudentLife dataset, Buffalo/phonelab-wifi dataset) show that, the proposed budgeted video replacement policy achieves a longer successfully delivered video length, compared with other general replacement policies. • We propose a budgeted video replacement policy in mobile video crowdsensing. • We formulate the video caching problem as a budgeted maximum coverage problem. • We propose a practical greedy solution and also infer the approximate ratio. • We conduct simulations based on two real-world traces. [ABSTRACT FROM AUTHOR]