The quality assessment for 4K super-resolution (SR) videos can be conducive to the optimization of video SR algorithms. To improve the subjective and objective consistency of the SR quality assessment, a 4K video database and a blind metric are proposed in this paper. In the database SR4KVQA, there are 30 4K pristine videos, from which 600 SR 4K distorted videos with mean opinion score (MOS) labels are generated by three classic interpolation methods, six SR algorithms based on the deep neural network (DNN), and two SR algorithms based on the generative adversarial network (GAN). The benchmark experiment of the proposed database indicates that video quality assessment (VQA) of the 4K SR videos is challenging for the existing metrics. Among those metrics, the Video-Swin-Transformer backbone demonstrates tremendous potential in the VQA task. Accordingly, a blind VQA metric based on the Video-Swin-Transformer backbone is established, where the normalized loss function and optimized spatio-temporal sampling strategy are applied. The experiment result manifests that the Pearson linear correlation coefficient (PLCC) and Spearman rank-order correlation coefficient (SROCC) of the proposed metric reach 0.8011 and 0.8275 respectively on the SR4KVQA database, which outperforms or competes with the state-of-the-art VQA metrics. The database and the code proposed in this paper are available in the GitHub repository, https://github.com/AlexReadyNico/SR4KVQA.