For the synthetic aperture digital holography, the effects of speckle noise on image registration accuracy based on the feature point matching are investigated. An experimental setup for the digital off-axis holography is established, and the scale-invariant feature transform (SIFT) algorithm and the speeded-up robust feature (SURF) algorithm are used to extract the feature points of the image to be matched and the reference image. The feature point matching is performed by the nearest neighbor search method based on Euclidean distance and the parameters of the image transformation model are estimated using the maximum likelihood estimation sample consensus algorithm. The experimental results show that the SIFT algorithm is more robust to speckle noise. For the SIFT algorithm, when the signal-to-noise ratio is greater than 1.4, the relative error of registration is less than 0.02, and for the SURF algorithm, when the signal-to-noise ratio is greater than 1.7, the relative error of registration is less than 0.05.