In this study, based on the random fuzzy theory, the random fuzzy multiobjective programming (RFMOP) problems are presented. We first consider its expected value model, and investigated its convexity. Then the expected-value efficient solution and the expected-value wake efficient solution are defined. To solve the RFMOP problem, the method of main objective function are proposed, whose theoretical results can provide foundation for designing solution algorithm. Finally, a numerical example are given to explain the method proposed above.