2-D shape descriptors, which are vectors representing characteristics of shapes, enable comparison and classification of shapes and are mainly applied to image and 3-D model retrieval. Existing descriptors have limitations that they only describe shapes of single closed contours or lack in precision, making it difficult to be applied to shapes with multiple contours. Therefore, in this paper, we propose a new shape descriptor called Multi-Curvature-Scale Space that can be applied to shapes with multiple contours. Specifically, we represent the topology of the sub-contours in the multi-contour along with Curvature-Scale Space descriptors to represent the shapes of each sub-contours. Also, by allowing the weight of each component to be controlled when computing the distance between descriptors the weight, we deal with ambiguities in measuring similarity between shapes. Results of various experiments that prove the effectiveness of proposed descriptor are presented.