Effectively describing and recognizing leaf shapes under arbitrary variations, particularly from a large database, remains an unsolved problem. In this research, we attempted a new strategy of describing leaf shapes by walking and measuring along a bunch of chords that pass through the shape. A novel chord bunch walks (CBW) descriptor is developed through the chord walking behavior that effectively integrates the shape image function over the walked chord to reflect both the contour features and the inner properties of the shape. For each contour point, the chord bunch groups multiple pairs of chords to build a hierarchical framework for a coarse-to-fine description that can effectively characterize not only the subtle differences among leaf margin patterns but also the interior part of the shape contour formed inside a self-overlapped or compound leaf. Instead of using optimal correspondence based matching, a Log-Min distance that encourages one-to-one correspondences is proposed for efficient and effective CBW matching. The proposed CBW shape analysis method is invariant to rotation, scaling, translation, and mirror transforms. Five experiments, including image retrieval of compound leaves, image retrieval of naturally self-overlapped leaves, and retrieval of mixed leaves on three large scale datasets, are conducted. The proposed method achieved large accuracy increases with low computational costs over the state-of-the-art benchmarks, which indicates the research potential along this direction.