A part-to-part curve matching approach for occluded object recognition is proposed since the global curve matching methods perform infeasible in occluded object recognition. First, a local curve feature descriptor called Affine Invariant Curve Descriptor (AICD) is constructed to represent the local shape of a curve. It is affine invariant based on curve affine invariant signature and its unsigned integral. Then, combining AICD with a curve segmentation strategy based on curvature zero crossing point, an affine invariant curve matching algorithm is developed. Experiments demonstrate that the proposed algorithm exhibits effectiveness in object recognition with affine deformation and partial occlusion and outperforms the state-of-art curve matching methods.