For project scheduling，when solving a cost problem，such as the time-cost tradeoff problem，we need to obtain the minimum cost of the project as a starting point of the optimization process. If only a single precedence relation exists between activities, we can obtain the minimum cost of a project by letting all activities choose their minimum cost durations．If generalized precedence relations (GPRs) exist between activities，letting all activities choose their minimum cost durations may not meet the given precedence relations and result in a unfeasible project. Aiming at the minimum cost problem of projects under GPRs，we found a mathematical model，and then transform it into an equivalent and special minimum cost maximum flow model by using primal-dual theory． Thus，we can calculate the optimal solution of the special minimum cost maximum flow model by using a current algorithm，and then obtain the minimum cost of a project under GPRs based on the primal-dual relation．