We propose a fluid-based registration framework of medical images based on implicit neural representation. By integrating implicit neural representation and Large Deformable Diffeomorphic Metric Mapping (LDDMM), we employ a Multilayer Perceptron (MLP) as a velocity generator while optimizing velocity and image similarity. Moreover, we adopt a coarse-to-fine approach to address the challenge of deformable-based registration methods dropping into local optimal solutions, thus aiding the management of significant deformations in medical image registration. Our algorithm has been validated on a paired CT-CBCT dataset of 50 patients,taking the Dice coefficient of transferred annotations as an evaluation metric. Compared to existing methods, our approach achieves the state-of-the-art performance.