Constituent Context Model (CCM) is an effective generative model for grammar induction, the aim of which is to induce hierarchical syntactic structure from natural text. The CCM simply defines the Multinomial distribution over constituents, which leads to a severe data sparse problem because long constituents are unlikely to appear in unseen data sets. This paper proposes a Bayesian method for constituent smoothing by defining two kinds of prior distributions over constituents: the Dirichlet prior and the Pitman-Yor Process prior. The Dirichlet prior functions as an additive smoothing method, and the PYP prior functions as a back-off smoothing method. Furthermore, a modified CCM is proposed to differentiate left constituents and right constituents in binary branching trees. Experiments show that both the proposed Bayesian smoothing method and the modified CCM are effective, and combining them attains or significantly improves the state-of-the-art performance of grammar induction evaluated on standard treebanks of various languages.