Topology-preserving geometric deformable models (TGDMs) are used to segment objects that have a known topology. Their accuracy is inherently limited by the resolution of the underlying computational grid. Although this can be overcome by using fine-resolution grids, both the computational cost and the size of the resulting surface increase dramatically. In this article, we present a new octree grid topology-preserving deformable model (OTGDM). OTGDMs refine grid resolution locally, thus maintaining computational efficiency and keep the surface mesh size manageable. Topology preservation is achieved by adopting concepts from a digital topology framework on octree grids that we have proposed previously. Details of OTGDM implementation are discussed, including grid generation, model initialization, numerical schemes, and final surface model extraction. Experiments on both mathematical phantoms and real medical images are used to demonstrate the advantages of OTGDMs.