Rendering novel views from captured multi-view images has made considerable progress since the emergence of the neural radiance field. This paper aims to further advance the quality of view rendering by proposing a novel approach dubbed the neural radiance feature field (NRFF). We first propose a multiscale tensor decomposition scheme to organize learnable features so as to represent scenes from coarse to fine scales. We demonstrate many benefits of the proposed multiscale representation, including more accurate scene shape and appearance reconstruction, and faster convergence compared with the single-scale representation. Instead of encoding view directions to model view-dependent effects, we further propose to encode the rendering equation in the feature space by employing the anisotropic spherical Gaussian mixture predicted from the proposed multiscale representation. The proposed NRFF improves state-of-the-art rendering results by over 1 dB in PSNR on both the NeRF and NSVF synthetic datasets. A significant improvement has also been observed on the real-world Tanks & Temples dataset. Code can be found at https://github.com/imkanghan/nrff.