Feature-based retinal fundus image registration (RIR) technique aligns fundus images according to geometrical transformations estimated between feature point correspondences. To ensure accurate registration, the feature points extracted must be from the retinal vessels and throughout the image. However, noises in the fundus image may resemble retinal vessels in local patches. Therefore, this paper introduces a feature extraction method based on a local feature of retinal vessels (CURVE) that incorporates retinal vessels and noises characteristics to accurately extract feature points on retinal vessels and throughout the fundus image. The CURVE performance is tested on CHASE, DRIVE, HRF and STARE datasets and compared with six feature extraction methods used in the existing feature-based RIR techniques. From the experiment, the feature extraction accuracy of CURVE (86.021%) significantly outperformed the existing feature extraction methods (p ≤ 0.001*). Then, CURVE is paired with a scale-invariant feature transform (SIFT) descriptor to test its registration capability on the fundus image registration (FIRE) dataset. Overall, CURVE-SIFT successfully registered 44.030% of the image pairs while the existing feature-based RIR techniques (GDB-ICP, Harris-PIIFD, Ghassabi’s-SIFT, H-M 16, H-M 17 and D-Saddle-HOG) only registered less than 27.612% of the image pairs. The one-way ANOVA analysis showed that CURVE-SIFT significantly outperformed GDB-ICP (p = 0.007*), Harris-PIIFD, Ghassabi’s-SIFT, H-M 16, H-M 17 and D-Saddle-HOG (p ≤ 0.001*).