I study a semiparametric Bayesian method for over-identified moment condition models. A mixture of parametric distributions with random weights is used to flexibly model an unknown data generating process. The random mixture weights are defined by the exponential tilting projection method to ensure that the joint distribution of the data distribution and the structural parameters are internally consistent with the moment restrictions. In this framework, I make several contributions to Bayesian estimation and inference, as well as model specification. First, I develop simulation-based posterior sampling algorithms based on Markov chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) methods. Second, I provide a method to compute the marginal likelihood and use it for Bayesian model selection (moment selection) and model averaging. Lastly, I extend the scope of Bayesian analysis for moment condition models. These generalizations include dynamic moment condition models with time-dependent data and moment condition models with exogenous dynamic latent variables.