To establish a proper contour description function is a prerequisite for various contour-based shape matching algorithms. local complex moment invariants of contour vertex were built according to complex moment theory, and relational expression between local complex moment invariants and origin coordinates of contour vertex was deduced. As a result, a new contour description function was established by combing local complex moment invariants with local curvature of feature points. Besides invariance and uniqueness, this new contour description function took global and local feature into account simultaneously, and had high computation efficiency because it only spent linear time on building it, and had strong anti-noise ability because it was only related to low order geometry moments. At last, string match method was utilized to match the contour of shape based on the new contour description function. Our experiments on Kimia database indicated that this contour description function and matching method had a better performance compared with the other contour matching method based on various contour description function. Key words: Shape Match; Contour Description Function; Complex Moments