A model for Program Evaluation and Review Technique (PERT) under fuzzy linguistic contexts is introduced. In this fuzzy linguistic PERT network model, each activity duration is represented by a fuzzy linguistic description. Aggregation and comparison of the estimated linguistic expectations of activity durations are manipulated by the techniques of computing with words (CW). To provide suitable contexts for this purpose, we first introduce several variations of basic linguistic labels of a linguistic variable, such as weighted linguistic labels, generalized linguistic labels and weighted generalized linguistic labels etc., and then based on the notion of canonical characteristic value (CCV) function of a linguistic variable, we develop some related CW techniques for aggregation and comparison of these linguistic labels. Afterward, using a computing technique of linguistic probability introduced by Zadeh and based on the new developed CW techniques for weighted generalized linguistic labels, we investigate the associated linguistic expectation PERT network of a fuzzy linguistic PERT network. Also, throughout the paper, several examples are used to illustrate related notions and applications