Many researchers have proposed portfolio models based on the stochastic and fuzzy approaches until now, and there are some models considering both random and ambiguous conditions, particularly using fuzzy random or random fuzzy variables. However, few studies with multiobjective random fuzzy models for the portfolio selection problems have been performed. Therefore, a multiobjective random fuzzy portfolio selection problem based on CAPM, which is one of the most standard factor models, is proposed. In the sense of mathematical programming, our proposed problems are not well-defined problems due to randomness and fuzziness. Therefore, setting some criterions and introducing chance constrains, main problems are transformed into deterministic programming problems. Finally, we construct a solution method to obtain a global optimal solution of the problem.