The matching between an open contour and a closed contour is a basis for the alignment of their common part and a similarity measure. We propose a coarse-to-fine method for partial shape matching, which does not need to scan the target shape, construct a codebook of model contour fragments, or depend on background support domains. For this purpose, a linearization algorithm for partial shapes is introduced to extract the initial shape segments from the closed contour those possibly match with the open contour. The next refining procedure of the coarse matching eliminates significantly dissimilar shape segments to reduce the further processing of fine matching. We propose a shape similarity description to finely describe the similarity between the open contour and the remaining shape segments. Finally, an order-preserving point injection between the open contour and the closed contour is established. Valuations of the proposed method on a benchmark dataset and real images demonstrate that the overall and component performances are excellent and robust to various disturbances and similarity transformations. Last, a gesture recognition application is implemented.