Incremental parsers have potential advantages for applications like language modeling for machine translation and speech recognition. We describe a new algorithm for incremental transition-based Combinatory Categorial Grammar parsing. As English CCGbank derivations are mostly right branching and non-incremental, we design our algorithm based on the dependencies resolved rather than the derivation. We introduce two new actions in the shift-reduce paradigm based on the idea of revealing (Pareschi and Steedman, 1987) the required information during parsing. On the standard CCGbank test data, our algorithm achieved improvements of 0.88% in labeled and 2.0% in unlabeled F-score over a greedy non-incremental shift-reduce parser.