Nowadays, in the competitive markets referring to the fast changes in the costumers’ needs and expectations, one of the essential decisions and strategic considerations for each organization is to determine the best research and development projects portfolio in order to keep its competitive abilities. In this paper, we considered “Research and Development (R&D) Project Portfolio Selection” as a multi-objective decision making in some special situations. In which, the decision makers (DMs) are not sure about the exact amount of each aspiration level, or it is impossible for them to calculate it at the first step of the projects. Our proposed model is based on a multi-choice goal programming method to let the DMs set multi-choice aspiration levels for each goal and help them to avoid underestimation of the decisions. This new approach can be used in many cases of the real world effectively. Furthermore, we used the proposed model in Saipa Group as a real case study.