Online dense mapping of urban scenes is of paramount importance for scene understanding of autonomous navigation. Traditional online dense mapping methods fuse sensor measurements (vision, lidar, etc.) across time and space via explicit geometric correspondence. Recently, NeRF-based methods have proved the superiority of neural implicit representations by high-fidelity reconstruction of large-scale city scenes. However, it remains an open problem how to integrate powerful neural implicit representations into online dense mapping. Existing methods are restricted to constrained indoor environments and are too computationally expensive to meet online requirements. To this end, we propose Swift-Mapping, an online neural implicit dense mapping framework in urban scenes. We introduce a novel neural implicit octomap (NIO) structure that provides efficient neural representation for large and dynamic urban scenes while retaining online update capability. Based on that, we propose an online neural dense mapping framework that effectively manages and updates neural octree voxel features. Our approach achieves SOTA reconstruction accuracy while being more than 10x faster in reconstruction speed, demonstrating the superior performance of our method in both accuracy and efficiency.