Dense 3D reconstruction from a stream of depth images is the key to many mixed reality and robotic applications. Although methods based on Truncated Signed Distance Function (TSDF) Fusion have advanced the field over the years, the TSDF volume representation is confronted with striking a balance between the robustness to noisy measurements and maintaining the level of detail. We present Bi-level Neural Volume Fusion (BNV-Fusion), which leverages recent advances in neural implicit representations and neural rendering for dense 3D reconstruction. In order to incrementally integrate new depth maps into a global neural implicit representation, we propose a novel bi-level fusion strategy that considers both efficiency and reconstruction quality by design. We evaluate the proposed method on multiple datasets quantitatively and qualitatively, demonstrating a significant improvement over existing methods.