Combinatory Categorial Grammar (CCG) is an expressive grammar formalism which is able to capture long-range dependencies. However, building large and wide-coverage treebank for CCG is expensive and time-consuming. In this paper, we focus on the problem of unsupervised CCG induction from plain texts. Based on the baseline model in (Bisk and Hockenmaier, 2012), we propose following two improvements: (1) we utilize boundary part-of-speech (POS) tags to capture lexical information; (2) we perform nonparametric Bayesian inference based on the Pitman-Yor process to learn compact grammars. Experiments on English Penn treebank demonstrate the effectiveness of our boundary model and Bayesian learning.