Free-Libre Open Source Software (FLOSS) tools are free-cost license highly attractive to be implemented by organizations. However, not of all the FLOSS tools are mature, and failed implementations can occur. Thus, FLOSS evaluation-selection frameworks and FLOSS success-failure implementation factors studies have been conducted. In this research, we advance on such studies through an integrated FLOSS evaluation-selection model with a risk-based decision making approach. Our model was built upon the other two literatures, and it was structured as a Multi-Attribute Decision Making (MADM) model which contains 12 variables grouped in four risk categories: financial, organizational, end-user and technical ones. We illustrated its utilization in the domain of Information Technology Service Management (ITSM) FLOSS tools. Hence, our model contributes to the FLOSS literature with the inclusion of the risk management approach and to the FLOSS evaluation-selection praxis with the provision of an innovative and essential risk-based model.