A skyline of a d-dimensional dataset contains the points that are not dominated by any other point on all dimensions. Due to its usefulness, a skyline query has recently received a considerable attention in several applications. However, as the number of dimensions increases, the probability of one point dominating another point becomes very low. In consequence, the number of points in the skyline becomes tremendous. To remedy this disadvantage, the k-dominant skyline has been introduced, which relaxes the domination relationship. Although the number of k-dominant skyline points is smaller than the number of skyline points, some important points in the dataset may be excluded from the result of a k-dominant skyline query due to the cyclic dominance relationship. With this problem in mind, we introduce a novel types of skyline queries, called the scored k-dominant skyline query. A scored k-dominant skyline is computed from skyline points by utilizing the notions of (i) k-dominance relationship and (ii) k-dominant score. We also present the search algorithm for the scored k-dominant skyline. Finally, we demonstrate the effectiveness of the scored k-dominant skyline through a set of simulations by using both real dataset and synthetic dataset.