Deep neural networks (DNNs) have demonstrated their outperformance in various software systems, but also exhibit misbehavior and even result in irreversible disasters. Therefore, it is crucial to identify the mis-behavior of DNN-based software and improve DNNs’ quality. Test input prioritization is one of the most appealing ways to guarantee DNNs’ quality, which prioritizes test inputs so that more bug-revealing inputs can be identified earlier with limited time and manual labeling efforts. However, the existing prioritization methods are still limited from three aspects: certifiability, effectiveness, and generalizability. To overcome the challenges, we propose CertPri, a test input prioritization technique designed based on a movement cost perspective of test inputs in DNNs’ feature space. CertPri differs from previous works in three key aspects: (1) certifiable: it provides a formal robustness guarantee for the movement cost; (2) effective: it leverages formally guaranteed movement costs to identify malicious bug-revealing inputs; and (3) generic: it can be applied to various tasks, data, models, and scenarios. Extensive evaluations across 2 tasks (i.e., classification and regression), 6 data forms, 4 model structures, and 2 scenarios (i.e., white-box and black-box) demonstrate CertPri’s superior performance. For instance, it significantly improves 53.97% prioritization effectiveness on average compared with baselines. Its robustness and generalizability are 1.41~2.00 times and 1.33~3.39 times that of baselines on average, respectively.