For a given set of moving objects, continuous k-nearest neighbor (CKNN) query q over moving objects is to quickly identify and monitor the k-nearest objects as objects and the query point evolve. In real life, many location-based applications in transportation, social network, e-commerce, and other fields involve the basic problem of processing CKNN queries over moving objects. Most of existing work processing CKNN queries usually needs to determine a query range containing k-nearest neighbors through multiple iterations, while each iteration has to identify the number of objects in the current query range, and which dominates the query cost. In order to address this issue, this study proposes a dual index called GGI that consists of a grid index and a Gaussian mixture function to simulate the varying distribution of objects. The bottom layer of GGI employs a grid index to maintain moving objects, and the upper layer constructs Gaussian mixture model to simulate the distribution of moving objects in two-dimensional space. Based on GGI, an incremental search algorithm called IS-CKNN to process CKNN queries. This algorithm directly determines a query region that at least contains k neighbors of q based on Gaussian mixture model, which greatly reduces the number of iterations. When the objects and query point evolve, an efficient incremental query strategy is further proposed, which can maximize the use of existing query results and reduce the calculation of the current query. Finally, extensive experiments are carried out on one real dataset and two synthetic datasets to confirm the superiority of the proposed proposal.