The neural radiance field (NeRF) achieved remarkable success in modeling 3D scenes and synthesizing high-fidelity novel views. However, existing NeRF-based methods focus more on the make full use of the image resolution to generate novel views, but less considering the generation of details under the limited input resolution. In analogy to the extensive usage of image super-resolution, NeRF super-resolution is an effective way to generate the high-resolution implicit representation of 3D scenes and holds great potential applications. Up to now, such an important topic is still under-explored. In this paper, we propose a NeRF super-resolution method, named Super-NeRF, to generate high-resolution NeRF from only low-resolution inputs. Given multi-view low-resolution images, Super-NeRF constructs a consistency-controlling super-resolution module to generate view-consistent high-resolution details for NeRF. Specifically, an optimizable latent code is introduced for each low-resolution input image to control the 2D super-resolution images to converge to the view-consistent output. The latent codes of each low-resolution image are optimized synergistically with the target Super-NeRF representation to fully utilize the view consistency constraint inherent in NeRF construction. We verify the effectiveness of Super-NeRF on synthetic, real-world, and AI-generated NeRF datasets. Super-NeRF achieves state-of-the-art NeRF super-resolution performance on high-resolution detail generation and cross-view consistency.