Stereo vision is a long-studied problem in computer vision. Yet, few have approached it from the angle of interpolation. In this paper, we present an approach, Interpolation-based Iterative Stereo Matching (IISM), that regards stereo matching as a mapping that maps image position from one view to the corresponding position in the other view, and the mapping is to be learned or interpolated from some samples that could be just some initial correspondences over some distinct image features that are easy to match. Once the mapping is interpolated, it could be used to predict correspondences beyond the samples, and once such predicted correspondences are corrected and confirmed through local search around the predicted positions in the image data, they could be used together with the original samples as a new and larger sample for another round of interpolation. In other words, interpolation for the mapping is not one-time, but about a number of rounds of interpolation, correspondence prediction, prediction correction, sample set enlargement, and so on, each round producing a more accurate stereo correspondence mapping. IISM utilizes the Example-Based Interpolation (EBI) scheme, but in IISM the existing EBI is adapted to ensure the established correspondences satisfy exactly the epipolar constraint of the image pair, and to a certain extent preserve discontinuities in the stereo disparity space of the imaged scene. Experimental results on a number of real image datasets show that the proposed solution has promising performance even when the initial correspondence samples are sparse.