The availability of free-libre open source software (FLOSS) has stimulated their organizational implementation in many countries. The main attractiveness for it is the free-cost license of usage regarding with acquisition of COTS (components of the shelf) commercial software, among other factors such as: maturity status, available technical community support, popularity, and compliance to international standards. However, not of the all FLOSS tools released from such FLOSS development projects achieve the expected qualities, and thus organizations interested in using them must conduct a careful evaluation-selection process. With this in mind, several evaluation-selection frameworks for FLOSS have been reported in the literature and some studies have identified a set of organizational factors associated to successful and failed utilizations of FLOSS tools in organizations. In this research, we elaborate a FLOSS Evaluation-Selection model by combining both sets of literature on FLOSS evaluation models and FLOSS implementation models. This model is implemented with a MADM (Multi-Attribute Decision-Making) risk-based mechanism. We illustrate this model with the evaluation-selection of a FLOSS tool in the domain of Information Technology Service Management (ITSM). Hence, this paper contributes to our body of knowledge with the provision of a simplified evaluation-selection model for FLOSS tools derived from two core sets of FLOSS literatures, under an innovative risk-based approach.