Edge-based tracking is a fast and plausible approach for textureless 3D object tracking, but its robustness is still very challenging in highly cluttered backgrounds due to numerous local minima. To overcome this problem, we propose a novel method for fast and robust textureless 3D object tracking in highly cluttered backgrounds. The proposed method is based on optimal local searching of 3D-2D correspondences between a known 3D object model and 2D scene edges in an image with heavy background clutter. In our searching scheme, searching regions are partitioned into three levels (interior, contour, and exterior) with respect to the previous object region, and confident searching directions are determined by evaluating candidates of correspondences on their region levels; thus, the correspondences are searched among likely candidates in only the confident directions instead of searching through all candidates. To ensure the confident searching direction, we also adopt the region appearance, which is efficiently modeled on a newly defined local space (called a searching bundle). Experimental results and performance evaluations demonstrate that our method fully supports fast and robust textureless 3D object tracking even in highly cluttered backgrounds.