To realize the digital elevation inversion of the interferometric imaging radar altimeter (InIRA), an interference complex images registration algorithm combining enhanced scale-invariant feature transform (SIFT) characteristics with correlation coefficient is proposed. First, the locally tuned nonlinear method is used to enhance the image features. Then, SIFT algorithm is used to extract the matched feature points that are used as control points after screening. Based on these control points, the affine transformation is applied to calculate the coarse matching relation. Second, multiple control points are chosen uniformly. The local accurate offsets are determined by interpolating and calculating the maximum of correlation coefficients. The least-squares method is used to fit the difference between the two images. Third, the two images are matched by interpolating and resampling the one to be registered. Finally, the simulated InIRA sea surface images and the Sentinel-1A images of the Mount Hua area are employed to experiment. The results show that the proposed algorithm combines the advantages of SIFT algorithm and correlation coefficient algorithm. It is robust and its registration accuracy is better than the particle swarm optimization sample consensus algorithm, unsupervised deep-learning algorithm, SIFT algorithm, and correlation coefficient algorithm.