This paper presents Neural Visibility Field (NVF), a novel uncertainty quantification method for Neural Radi-ance Fields (NeRF) applied to active mapping. Our key insight is that regions not visible in the training views lead to inherently unreliable color predictions by NeRF at this region, resulting in increased uncertainty in the synthesized views. To address this, we propose to use Bayesian Networks to composite position-based field uncertainty into ray-based uncertainty in camera observations. Consequently, NVF nat-urally assigns higher uncertainty to unobserved regions, aiding robots to select the most informative next viewpoints. Extensive evaluations show that NVF excels not only in un-certainty quantification but also in scene reconstruction for active mapping, outperforming existing methods. More de-tails can be found at https://sites.google.com/view/nvf-cvpr24/.