Under the fuzzy random environment and aimed at the properties of multi-objective programming, this paper gains many important conclusions. Based on the fuzzy random theory, the expected value model of fuzzy random multi-objective programming is presented which transforms the uncertainties of practical problems into the certainties and provides the theoretical foundation for solving the real-life world problem. As we known, the convexity of programming problem plays an important part in optimization theory, this paper strictly proves the convexity of the model presented above by the properties of expectation of fuzzy random variable. Furthermore, this paper defines the concepts of expected-value non-inferior i.e. the expected-value absolutely optimal solution, the expected-value efficient solution and the expected-value wake efficient solution, and also investigates their properties. To solve the model of fuzzy random programming established by the real problem in practice, the conclusions obtained in this paper provide a theoretical foundation for designing algorithms and making the optimal decisions.