Abstract Aimed at sufficiently utilizing available data and prior distribution information, we introduce a data-driven Bayesian-type approach to solve multi-stage convex stochastic optimization, which can easily cope with the uncertainty about data process’s distributions and their inter-stage dependence. To unravel the properties of the proposed multi-stage Bayesian expectation optimization (BEO) problem, we establish the consistency of optimal value functions and solutions. Two kinds of algorithms are designed for the numerical solution of single-stage and multi-stage BEO problems, respectively. A queuing system and a multi-stage inventory problem are adopted to numerically demonstrate the advantages and practicality of the new framework and corresponding solution methods, compared with the usual formulations and solution methods for stochastic optimization problems.