The advancement of Wi-Fi and GPS technologies contribute a lot to location-based services (LBSs) that deliver services based on the geographic location. One of the most popular LBS applications is a moving k-range nearest neighbor (MkRNN) search. In road networks, a moving k-range nearest neighbor (kRNN) queries locate the k-NN for all the points that are found on the road segments, in a given spatial region defined by the user, based on the network distance. This is a significant task because the user’s location information may be inaccurate; furthermore, users may be unwilling to reveal their exact location for privacy reasons. Therefore, under this type of specific situation, evaluating the query results at each timestamp will create significant burden for the client. We therefore propose an efficient approach for computing a safe segment region and the safe exit points of a moving k-range nearest neighbor (MkRNN) query in a directed and dynamic road network. The safe region of a query is an area where the query result remains unchanged, so that the client is not required to evaluate the query answer returned by the location-based server (LBS) within the safe segment region. In addition, our safe-region-based query processing algorithm is designed for a directed and road network, in which each road network has exactly one defined direction and the network distances are not symmetric and dynamic road network, in which the time elapsed to travel each road segment, differs based on the traffic condition at some particular time. In contrast, previous kRNN research has produced algorithms that operate only in undirected road networks.