In this paper, the concept of gradient order is introduced and a novel gradient order curve descriptor (GOCD) for curve matching is proposed. The GOCD is constructed in the following main steps: firstly, curve support region independent of the dominant orientation is determined and then divided into several sub-regions based on gradient magnitude order; then gradient order feature (GOF) of each feature point is generated by encoding the local gradient information of the sample points; the descriptor is finally achieved by turning to the description matrix of GOF. Since both the local and the global gradient information are captured by GOCD, it is more distinctive and robust compared with the existing curve matching methods. Experiments under various changes, such as illumination, viewpoint, image rotation, JPEG compression and noise, show the great performance of GOCD. Furthermore, the application of image mosaic proves GOCD can be used successfully in actual field.