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A Bayesian network is a graphical model for representing probabilistic relationships among a set of variables. It is an important model for business analysis. Bayesian network learning methods have been applied to business analysis where data privacy is not considered. However, how to learn a Bayesian network over private data presents a much greater challenge. In this paper, we develop an approach to tackle the problem of Bayesian network induction on private data which may contain missing values. The basic idea of our proposed approach is that we combine randomization technique with Expectation Maximization (EM) algorithm. The purpose of using randomization is to disguise the raw data. EM algorithm is applied for missing values in the private data set. We also present a method to conduct Bayesian network construction, which is one of data mining computations, from the disguised data.