Extracting tubular structures from images is a widespread and challenging task in computer vision. To explore these continuous structures, iterative tracing methods offer a promising direction. However, in scenes with dense and blurred branches, existing tracing methods tend to jump to adjacent branches during tracing process, leading a significant topological mistake. The reason of this shortcoming is that the tracing model only focuses on the estimation of discrete nodes and ignores their connection attribution. To solve this problem, we introduce NETracer, a topology-aware iterative tracing method to improve the continuity and topological accuracy. In our approach, a node-edge estimation network with local connectivity loss is trained to produce the future nodes and their connective edges. Then, a geodesic distance-based search strategy is employed with the help of predicted edge cues to trace the future branches more accurately. Additionally, to comprehensively assess the effect of the tracing model, an new tracing metric is proposed to evaluate the local accuracy, continuity, and topological correctness of the traced branches. We demonstrate that our proposed method outperforms existing segmentation and tracing methods on five 2D road, vessel and 3D neuron datasets.