This paper applies the uncertainty theory to the time-cost trade-off problem due to various uncertain factors in real project. In practice, the overlapping relationships among some activities usually exist in the project. In order to simplify the calculation, the relationships are converted into the delay time and introduced to the formula of the project time. Then, the uncertain time-cost trade-off model with delay time is built. Meanwhile, the equivalent form of the uncertain programming model is given and proven to solve the proposed model. Finally, a project case is used to illustrate the effectiveness of the proposed model.