A search method and apparatus for a navigation system finds accessible points of interest (POI) along the route to the destination in a flexible manner. The navigation system changes its search range when the geographic condition warrants expansion of the search range. The search method is comprised of the steps of: searching POIs specified by a user along a route to a destination within a predetermined search range relative to the route, detecting POIs located within the predetermined search range, determining if a geographic condition on a specific area on the route exists that enables easy accessibility to POIs, expanding the search range if the geographic condition enabling the easy accessibility to POIs exists for the specific area, and detecting POIs located within the expanded search range.