Perceptual video super-resolution aims at converting low-resolution videos to visually appealing high-resolution ones. It may lead to temporal inconsistency due to the drastically changing outputs. In this paper, we propose cascaded sliding-window-based relativistic GAN (Generative Adversarial Network) fusion for perceptual and consistent video super-resolution (PC-VSR). Firstly, cascaded sliding-window-based relativistic GAN is designed to extract more useful information. It enlarges the temporal receptive field of sliding-window-based model in each step. It is able to enhance perceptual quality and compensate temporal consistency progressively and sufficiently. The trained separate refinement generator networks are fused into a final refinement generator. The final refinement generator can be calculated recursively at the testing stage. With our generator fusion, the parameter number is reduced and good quality is maintained. Extensive experimental results demonstrate that our approach outperforms state-of-the-art super-resolution methods in terms of perceptual quality. Our method also achieves good temporal consistency and per-pixel accuracy, compared with other perceptual approaches.