The present invention relates to a method of computing the result of a moving range query and the locations of safe exits in a road network and, more particularly, to a method and apparatus that receive a range query request from a moving client terminal and that provide a range query result, a safe region in which the range query result is maintained, and the locations of safe exits. The present invention provides a method in which a server provides a first query processing result and information about a safe region that provides a range query result identical to the first query result, thereby minimizing communication between a server and a client terminal when the client terminal is located in the safe region.