Shape matching has many applications in computer vision, such as shape classification, object recognition, object detection, and localization. In 2D cases, shape instances are 2D closed contours and matching two shape contours can usually be formulated as finding a one-to-one dense point correspondence between them. However, in practice, many shape contours are extracted from real images and may contain partial occlusions. This leads to the challenging partial shape matching problem, where we need to identify and match a subset of segments of the two shape contours. In this paper, we propose a new MCMC (Markov chain Monte Carlo) based algorithm to handle partial shape matching with mildly non-rigid deformations. Specifically, we represent each shape contour by a set of ordered landmark points. The selection of a subset of these landmark points into the shape matching is evaluated and updated by a posterior distribution, which is composed of both a matching likelihood and a prior distribution. This prior distribution favors the inclusion of more and consecutive landmark points into the matching. To better describe the matching likelihood, we develop a contour-subdivision technique to highlight the contour segment with highest matching cost from the selected subsequences of the points. In our experiments, we construct 1,600 test shape instances by introducing partial occlusions to the 40 shapes chosen from different categories in MPEG-7 dataset. We evaluate the performance of the proposed algorithm by comparing with three well-known partial shape matching methods.