Skyline queries are extensively incorporated in various real-life applications by filtering uninteresting data objects. Sometimes, a skyline query may return so many results because it cannot control the retrieval conditions especially for highdimensional datasets. As an extension of skyline query, the kdominant skyline query reduces the control of the dimension by controlling the value of the parameter kto achieve the purpose of reducing the retrieval objects. In addition, with the continuous promotion of Bigdata applications, the data we acquired may not have the entire content that people wanted for some practically reasons of delivery failure, no power of battery, accidental loss, so that the data might be incomplete with missing values in some attributes. Obviously, the k-dominant skyline query algorithms of incomplete data depend on the user definition in some degree and the results cannot be shared. Meanwhile, the existing algorithms are unsuitable for directly used to the incomplete big data. Based on the above situations, this paper mainly studies k-dominant skyline query problem over incomplete dataset and combines this problem with the distributed structure like MapReduce environment. First, we propose an index structure over incomplete data, named incomplete data index based on dominate hierarchical tree (ID-DHT). Applying the bucket strategy, the incomplete data is divided into different buckets according to the dimensions of missing attributes. Second, we also put forward query algorithm for incomplete data in MapReduce environment, named MapReduce incomplete data based on dominant hierarchical tree algorithm (MR-ID-DHTA). The data in the bucket is allocated to the subspace according to the dominant condition by Map function. Reduce function controls the data according to the key value and returns the k-dominant skyline query result. The effective experiments demonstrate the validity and usability of our index structure and the algorithm.