In this paper, we propose a new shape-coding algorithm called wavelet-based shape coding (WBSC). Performing wavelet transform on the orientation of original planar curve gives the corners called corner-1 points and end of arcs that belong to the original curve. Each arc is represented by a broken line and the corners called corner-2 points of the broken line are extracted. A polygonal approximation of a contour is an ordered list of corner-1 points, ends of arcs and corner-2 points which are extracted by using the above algorithm. All of the points are called polygonal vertices which will be compressed by our adaptive arithmetic encoding. Experimental results show that our method reduces code bits by about 26% compared with the context-based arithmetic encoding (CAE) of MPEG-4, and the subjective quality of the reconstructed shape is better than that of CAE at the same Dn.