Korean has a large set of characters, and has a two-dimensional formation: each character is composed of graphemes in two dimensions. Whereas connections between characters are rare, connections inside a grapheme and between graphemes happen frequently and these connections generate many cursive strokes. To deal with the large character set and the cursive strokes, using the graphemes as a recognition unit is an efffective approach, because it naturally accommodates the structural characteristics of the characters. In this paper, we propose a grapheme-based on-line recognition method for cursive korean characters. Our method uses a TDNN recognition engine to segment cursive strokes into graphemes and a graph-algorithmic postprocessor based on korean grapheme composition rule and viterbi search algorithm to find the best recognition score path. We experimented the method on freely hand-written charactes and obtained a recognition rate of 94.5%.