In this paper, we propose a novel recognition model of on-line cursive Korean characters using the hidden Markov model (HMM) and a level building algorithm. The model is constructed as a form of recognition network with HMMs for graphemes and Korean combination rules. Though the network represents the large character set efficiently and is flexible enough to accommodate variability of input patterns, it has a problem of recognition speed, caused by 11,172 search paths. To solve the problem, we modify a level building algorithm to be adapted directly to the Korean combination rules and apply it to the model. The modified algorithm is an efficient network search procedure, the time complexity of which depends on the number of grapheme HMMs and ligature HMMs, not the number of paths in the extensive recognition network. A test with 20,000 handwritten characters shows a recognition rate of 90.2% and speed of 0.72 s per character. (C) 1997 Pattern Recognition Society.