In this paper, an affine invariant curve matching method using curvature scale-space and normalization is proposed. Prior to curve matching, curve normalization with respect to affine transformations is applied, allowing a lossless affine invariant curve representation. The maxima points of the curvature scale-space (CSS) image are then used to represent the normalized curve, while retaining the local properties of the curve. The matching algorithm that follows, matches the maxima sets of CSS images and the resulting matching cost provides a measure of similarity. The method’s performance and robustness is evaluated through a variety of curves and affine transformations, obtaining precise shape similarity and retrieval.