Mammals have ability to perform accurate and robust path integration-based metric navigation even in the absence of visual or other environmental cues, which provides a new idea to find brain-inspired solutions to tackle the problems of serious drift of IMU-based inertial navigation of UAV when the external sensory cues are not available. Multi-scale grid cells in the medial entorhinal cortex are thought to be a fundamental portion of mammals’ ability to perform 3D path integration-based metric navigation. This paper studies and presents, for the first time, a neural system to implement path integration-based metric navigation in 3D environments integrating networks of encoding and decoding multi-scale grid cells using neural dynamic models, i.e. three-dimensional continuous attractor network and neural cliques, respectively. Experimental results show the neural system can successfully path integrate self-motion information for large-scale 3D navigation and provides robust and error-correcting position information, displaying possible neural solution to overcome serious drift of IMU-based inertial navigation of UAV in the absence of external sensory cues.