Neural Radiance Fields (NeRF) and its variants have reached state-of-the-art performance in many novel-view-synthesis-related tasks. However, current NeRF-based methods still suffer from the existence of reflective objects, often resulting in blurry or distorted rendering. Instead of calculating a single radiance field, we propose a multispace neural radiance field (MS-NeRF) that represents the scene using a group of feature fields in parallel sub-spaces, which leads to a better understanding of the neural network toward the existence of reflective and refractive objects. Our multi-space scheme works as an enhancement to existing NeRF methods, with only small computational overheads needed for training and inferring the extra-space outputs. We demonstrate the superiority and compatibility of our approach using three representative NeRF-based models, i.e., NeRF, Mip-NeRF, and Mip-NeRF 360. Comparisons are performed on a novelly constructed dataset consisting of 25 synthetic scenes and 7 real captured scenes with complex reflection and refraction, all having 360-degree viewpoints. Extensive experiments show that our approach significantly outperforms the existing single-space NeRF methods for rendering high-quality scenes concerned with complex light paths through mirror-like objects.