•Project portfolio selection is a complex and difficult task in fuzzy environments.•A three-stage hybrid method is used to select an optimal combination of projects.•Data Envelopment Analysis is used to screen the available projects.•TOPSIS is used to rank the potentially promising projects.•Linear Integer Programming is used to select the most suitable project portfolio. Project selection and resource allocation are critical issues in project-based organizations. These organizations are required to plan, evaluate, and control their projects in accordance with the organizational mission and objectives. In this study, we propose a three-stage hybrid method for selecting an optimal combination of projects. We obtain the maximum fitness between the final selection and the project initial rankings while considering various organizational objectives. The proposed model is comprised of three stages and each stage is composed of several steps and procedures. We use Data Envelopment Analysis (DEA) for the initial screening, the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) for ranking the projects, and linear Integer Programming (IP) for selecting the most suitable project portfolio in a fuzzy environment according to organizational objectives. Finally, a case study is used to demonstrate the applicability of the proposed method and exhibit the efficacy of the algorithms and procedures.