In this paper, a word segmentation method for handwritten Korean text line images is proposed. The method uses gap information to segment words in line images, where the gap is defined as a white run obtained after vertical projection of line images. Each gap is assigned to one of inter-word gap and inter-character gap based on gap distance. We take up three distance measures which have been proposed for the word segmentation of handwritten English text line images. Then we test three clustering techniques to detect the best combination of gap metrics and classification techniques for Korean text line images. The experiment has been done with 305 text line images extracted manually from live mail pieces. The experimental result demonstrates the superiority of BB(Bounding Box) distance measure and sequential clustering approach, in which the cumulative word segmentation accuracy up to the third hypothesis is 88.52%. Given a line image, the processing time is about 0.05 second.