Enterprises have become increasingly driven by the management of their project portfolios. This trend can be observed by the emergence of international standards, models and compilations of best practices, such as the ISO/IEC 12207, the Standard for Portfolio Management by the Project Management Institute, and the MR MPS. Among the existing processes for Project Portfolio Management, the project selection activity has been a focal point, due not only to its relevance in the process as a whole, but also because of the low performance levels that the enterprises have been demonstrating in this task. The Modern Portfolio Theory developed by Harry Markowitz on the decade of 1952 is a widely used theory in Economy to select financial assets portfolios. However, there are some obstacles to adapt the economic concepts underlying this theory to the context of projects. This work aims to present an approach to support the selection of software project portfolios based on the Modern Portfolio Theory. Thus, a process was defined, a tool was developed to support the proposed approach, and experimental studies were conducted to compare the performance of the approach to other techniques that are currently used in the industry. The conclusion at the end of the work is that the proposed approach presents some evidence of a better performance than other existent techniques.