The Korean Combinatory Categorial Grammar (KCCG) tbrmalism can unitbrmly handle word order variation among arguments and adjuncts within a clause as well as in complex clauses and across clause boundaries, i.e., long distance scrambling. Ill this paper, incremental parsing technique of a morpheme graph is developed using the KCCG. We present techniques for choosing the most plausible parse tree using lexical information such as category merge probability, head-head co-occurrence heuristic, and the heuristic based on the coverage of subtrees. The performance results for various models for choosing the most plausible parse tree are compared.