This paper presents a quasi-dense matching algorithm between images based on the match propagation principle. The algorithm starts from a set of sparse seed matches, then propagates to the neighboring pixels by the best-first strategy, and produces a quasi-dense disparity map. The quasi-dense matching aims at broad modeling and visualization applications which rely heavily on matching information. Our algorithm is robust to initial sparse match outliers due to the best-first strategy. It is efficient in time and space as it is only output sensitive. It handles half-occluded areas because of the simultaneous enforcement of newly introduced discrete 2D gradient disparity limit and the uniqueness constraint. The properties of the algorithm are discussed and empirically demonstrated. The quality of quasi-dense matching are validated through intensive real examples.