In this paper,variational inference is studied on manifolds with certain metrics.To solve the problem,the analysis is first proposed for the variational Bayesian on Lie group,and then extended to the manifold that is approximated by Lie groups.Then the convergence of the proposed algorithm with respect to the manifold metric is proved in two iterative processes:variational Bayesian expectation (VB-E) step and variational Bayesian maximum (VB-M) step.Moreover,the effective of different metrics for Bayesian analysis is discussed.