Recently, due to the advanced technologies of mobile devices and wireless communication, there are many studies on telematics and LBS(location-based service) applications. because moving objects usually move on spatial networks, their locations are updated frequently, leading to the degradation of retrieval performance. To manage the frequent updates of moving objects' locations in an efficient way, a new distributed grid scheme, called DS-GRID (distributed S-GRID), and k-NN(k-nearest neighbor) query processing algorithm was proposed[1]. However, the result of k-NN query processing technique may be invalidated as the location of query and moving objects are changed. Therefore, it is necessary to study on continuous k-NN query processing algorithm. In this paper, we propose both MCE-CKNN and MBP(Monitoring in Border Point)-CKNN algorithmss are S-GRID. The MCE-CKNN algorithm splits a query route into sub-routes based on cell and seproves retrieval performance by processing query in parallel way by. In addition, the MBP-CKNN algorithm stores POIs from the border points of each grid cells and seproves retrieval performance by decreasing the number of accesses to the adjacent cells. Finally, it is shown from the performance analysis that our CKNN algorithms achieves 15-53% better retrieval performance than the Kolahdouzan's algorithm.