A continuous nearest neighbor (CNN) query retrieves the nearest neighbor of every point on a line segment and indicates its valid segments. Zheng et al. have proposed a Hilbert-curve index for the CNN query. This method contains two phases, searching candidates in the approximate search range, and filtering the candidates to get the final answer. However, it may determine a wide search range in the first phase based on this method, resulting in the decrease of the accuracy and the increase of the processing time. Therefore, in this paper, to avoid this disadvantage, we propose a forward moving method to efficiently support the CNN queries. The proposed method locally expands the search range along the query line segment to find the neighbors. Experimental results show that our method outperforms Zheng et al.’s method in terms of the accuracy and the processing time.