selecting an efficient project portfolio among available projects is a vital decision for any project manager. The main questions are which projects can have more long-term benefits for managers or organizations. Due to the complexity of this field of research, today so many approaches are developed for project selection. Calculation time and the quality of results are two main criteria that almost all researchers have considered on them. In this research, a new hybrid genetic algorithm with new heuristic mutation and cross-over is developed to choose a good portfolio of available projects. The presented algorithm is fast and effective to reach a good result in a reasonable time. Finding a good point to start as an initial population and using a good operator a heuristic mutation and cross-over are the main points of our algorithm. To check the quality of results we compare the developed algorithms with some recent ones in the literature and comparison studies and statistical calculation demonstrate the efficiency of the new genetic algorithm to select a good portfolio.