The k-nearest neighbor （kNN） query over moving objects is one of the important research topics in Location-Based Service （LBS）. Unlike kNN queries with a single query point， when a large number of query points issue query requests simultaneously， the same moving object may appear in the query results of multiple query points. This situation is called query result conflict， and multiple kNN queries involved in such conflicts are called conflict-aware kNN queries. In practical applications， the same moving object involved in query result conflicts cannot be assigned to multiple queries simultaneously. Instead， each query must retrieve k moving objects that differ from the results of other queries. Therefore， a globally optimized algorithm for conflict-aware kNN queries named RBCS-KNN （Road-Based Conflict Sensitive K Nearest Neighbor query algorithm） was proposed for road networks. Firstly， a two-layer index structure was built on the basis of the road network subgraphs after dividing. Secondly， by subgraph expansion and pruning strategies， the candidate conflicting query points were screened rapidly. Thirdly， kNN for the candidate query points were computed， and a sufficient number of candidate objects were expanded， while all conflicting query points were grouped dynamically. Finally， an optimal assignment solution was determined via an improved assignment strategy by which the sum of the distance from every query point to its k moving objects was minimized. Experimental results on multiple real-world datasets show that RBCS-KNN reduces the total query distance by 10% compared to the GLAD （Grid based LAbelling with scheDuling） algorithm， demonstrating its correctness and good performance.