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Based on the classical problem of project portfolio selection (PPS), the multi-phase rolling model of PPS was constructed under uncertainty, the objective was maximization of benefits of each phase. Related constraints were built relying both matching of strategy equilibrium between enterprise strategy requirement and synthesis of strategy contribution of projects which were selected, and the enhancement effect of resources. Upper-side and down-side nearness were put up based on fuzzy theory, and was used to measured the matching of strategy equilibrium. A crisp transformation was implemented with the fuzzy model based on possibility theory. Genetic algorithm was presented to solved the model, through development of path relinking (PR), the algorithm of successive substitute and successive retroposition was designed to applied to 0-1 encoding as local search, and get the better solution. Simulation test show that when project portfolio selection of multi phase rolling is doing, enterprise can get benefits steadily during five phases, and benefits is differentiate in 6-8 phases. This conclusion can help enterprise adjust its strategy periods. Statistics about numbers of project styles are selected in every phase show the periodic regularity. Research resultion can give a guidance to execution of project portfolio selection in fact. [ABSTRACT FROM AUTHOR]