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As a major type of continuous spatial queries, the moving k nearest neighbor (kNN) query has been studied extensively. However, most existing studies have focused on only the query efficiency. In this paper, we consider further the usability of the query results, in particular the diversification of the returned data points. We thereby formulate a new type of query named the moving k diversified nearest neighbor query (MkDNN). This type of query continuously reports the k diversified nearest neighbors while the query object is moving. Here, the degree of diversity of the kNN set is defined on the distance between the objects in the kNN set. Computing the k diversified nearest neighbors is an NP-hard problem. We propose an algorithm to maintain incrementally the k diversified nearest neighbors to reduce the query processing costs. We further propose two approximate algorithms to obtain even higher query efficiency with precision bounds. We verify the effectiveness and efficiency of the proposed algorithms both theoretically and empirically. The results confirm the superiority of the proposed algorithms over the baseline algorithm. [ABSTRACT FROM PUBLISHER]